![achieves deep sharing of both computation and resources, and it is fact-to-dimension joins and selection predicates. A join predicate
well suited to the characteristics of modern DW platforms: star F 1 Ddj has the standard form of a key/foreign-key equi-join. A
schema design, many-core systems, fast sequential scans, and large selection predicate cj can be arbitrarily complex (e.g., contain dis-
main memories. Using C JOIN as the basis, we build a query pro- junction or sub-queries), but can reference solely the tuple variable
cessing engine that scales gracefully to highly concurrent, dynamic of Ddj from the star query. For convenience of notation, we set cj
workloads. The query engine employs a single physical plan that to TRUE if the query does not place a predicate on the correspond-
is “always on” and is optimized continuously based on run-time ing table. Note that we allow for the case where B = ∅ (i.e., there
statistics. A new query can latch onto the single plan at any point is no GROUP BY clause, so either k = 0 or A = ∅) or A = ∅.
in time, and it immediately starts sharing work with concurrent In the remainder of the paper, we assume the most general case,
queries in the same plan. This deep, aggressive sharing is key to where A = ∅, B = ∅, and k > 0.
C JOIN’s efficiency and sets it apart from prior work. Problem Statement. We consider the problem of efficiently eval-
Measurements indicate that C JOIN achieves substantial improve-
uating a large number of concurrent star queries in a single data
ment over state-of-the-art commercial and research systems. For
warehouse. These queries can either be submitted directly by users,
256 concurrent queries on a star schema, C JOIN outperforms ma- or constitute sub-plans of more complex queries.
jor commercial and open-source systems by a factor of 10 to 100 An effective solution to this problem should yield high query
on the Star Schema Benchmark [17]. For 32 concurrent queries, throughput, as well as enable graceful degradation of query re-
C JOIN outperforms them by up to 5x. More importantly, when sponse time as the number of concurrent queries increases (i.e.,
going from 1 to 256 concurrent queries, C JOIN’s response time in-
avoid thrashing). This goal also implies a notion of predictability:
creases by less than 30%, compared to over 500% for a leading
Query response time should be determined primarily by the char-
commercial system. acteristics of the query, and not by the presence or absence of other
The rest of the paper is structured as follows: §2 describes our queries executing concurrently in the system. Existing general-
target data warehousing setting and summarizes related work; §3 purpose DWs do not fare well in this setting, hence our motivation
details the C JOIN operator and the new query processing engine
to find a solution suitable for highly concurrent data warehouses.
built around it; §4 describes the deployment of C JOIN on modern
We emphasize that the overall workload need not be restricted
DW platforms; §5 presents several extensions; §6 evaluates various
solely to star queries. On the contrary, we envision a system archi-
aspects of performance and scalability; and §7 concludes. tecture where concurrent star queries are diverted to a specialized
query processor (such as the one presented in this paper) and any
2. BACKGROUND AND STATE OF THE ART other SQL queries and update statements are handled using conven-
In this section, we provide background on the central problem tional infrastructure. While it is clearly desirable to support high
addressed in our paper: improving support for concurrent queries concurrency across all types of queries, there are significant chal-
in large data warehouses (§2.1). We then survey related work that lenges even in doing so for just the subset of star queries. Moreover,
has approached this or similar challenges (§2.2). this focus does not restrict the practicality of our solution, since star
queries are common in DW workloads. Finally, our query evalua-
2.1 Our Target Domain tion techniques can be employed as sub-plans, to evaluate the star
Data Warehousing Model. Below, we describe the model targeted “portion” of more complex queries.
by our solution; in §5 we show how specific assumptions behind Physical Data Storage. We develop our techniques assuming that
this model can be lifted without affecting our techniques. the DW employs a conventional row-store for data storage. This as-
We consider a DW that organizes information using a star schema, sumption is driven by the design of existing commercial DW solu-
which has become standard in the data warehousing industry. We tions, including Oracle, IBM, Microsoft, Teradata, and the product
assume a fact table F that is linked through foreign keys to d di- within which C JOIN was developed. However, our approach can
mension tables D1 , . . . , Dd . Following common practice, we as- be applied equally well to different architectures. For instance, it
sume that F is too large to fit in main memory and is considerably is possible to implement C JOIN within a column store or a system
larger than the dimension tables. employing compressed tables. We examine these cases in §5.
The warehouse supports a workload of SQL queries, including We do not make any specific assumptions about the physical de-
periodic updates. Following common industrial practice, we as- sign of the DW, such as partitioning, existence of indices, or mate-
sume that the concurrency control protocol provides snapshot iso- rialized views. However, as we show in §5, C JOIN can take advan-
lation guarantees. In this setting, each transaction is “tagged” with tage of existing physical structures (e.g., fact table partitioning).
a snapshot identifier, which is inherited by each query and update
statement in the transaction. 2.2 Related Work
We distinguish the class of SQL star queries that are common Our work builds builds upon a rich body of prior research and in-
in DW workloads, particularly in ad-hoc data analytics. As will dustrial efforts in addressing the concurrency problem. We review
be seen later, this specific query structure enables us to develop here primarily techniques that enable work sharing, which is key in
efficient techniques for answering concurrent queries. Formally, a achieving high processing throughput.
star query conforms to the following template:
Multi-Query Optimization. When a batch of queries is optimized
SELECT A, Aggr 1 , . . . , Aggr k as a unit, it becomes possible to identify common sub-expressions
FROM F , Dd1 ,. . . ,Ddn
V V and generate physical plans that share the common computation [21].
WHERE F 1 Ddj AND σcj (Ddj ) AND σc0 (F ) This approach requires queries to be submitted in batches, which
1≤j≤n 1≤j≤n
is incompatible with ad-hoc decision support queries. Moreover,
GROUP BY B
common computation can be factored only within the batch of opti-
Symbols A and B denote attribute sets from the referenced ta- mized queries, thus making it impossible to share work with queries
bles, and Aggr 1 , . . . , Aggr k are standard SQL aggregate functions, that are already executing. In contrast, our approach shares work
e.g., MIN, MAX, AVG. The WHERE clause is a conjunction of among the currently executing queries regardless of when they were
2](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-2-320.jpg)
![submitted and without requiring batch submission. query using the same plan—a single pass over a fully de-normalized,
Work Sharing. Staged database systems [11, 12] enable work in-memory fact table—thus incurring more or less the same ex-
sharing at run-time through an operator-centric approach. Essen- ecution cost. C JOIN achieves a similar goal, in that it enables
tially, each physical operator acts as a mini query engine that ser- predictable execution times for star queries. The key differences
vices several concurrent queries, which in turn enables dynamic compared to BLINK are that we do not require the database to
be memory-resident, we do not require the fact table to be de-
work sharing across several queries. A hash join operator, for in-
normalized, and our design directly supports high query concur-
stance, can share the build phase of a relation that participates in
different hash joins in several queries. This design was shown to rency, whereas BLINK targets the execution of one query at a time.
scale well to tens of complex queries. Our approach adopts a sim-
ilar work-sharing philosophy, but customizes it for the common 3. THE CJOIN PIPELINE
class of star queries. As a result, our design can scale to a sub- This section details the design of C JOIN. We first provide an
stantially larger number of concurrent queries. overview of C JOIN, using an illustrative example (§3.1) and then
In the Redbrick DW [9], a shared scan operator was used to share describe the various components in more detail (§3.2-§3.4). For
disk I/O among multiple scan operations executing concurrently on clarity, we initially assume a query-only workload that references
multiple processors; however, the in-memory data and the state of the same snapshot of the data. We then expand our discussion to
other operators were not shared. Cooperative scans [24] improve mixed workloads of both queries and updates in §3.5.
data sharing across concurrent scans by dynamically scheduling
queries and their data requests, taking into account current sys- Notation. In what follows, we write Q to denote the set of con-
tem conditions. Qiao et al. [18] have investigated shared memory current star queries that are being evaluated. We assume that each
scans as a specific form of work sharing in multi-core systems: by query is assigned a unique positive integer identifier, and we use
scheduling concurrent queries carefully, tuple accesses can be co- Qi to denote the query with id i. These identifiers are specific to
ordinated in the processor’s cache. Our approach also leverages a C JOIN and can be assigned when queries are registered with the
form of scan sharing, but targets large warehouses, where the fact operator. Also, an identifier can be reused after a query finishes its
relation cannot fit in main memory. In addition to I/O, our approach evaluation. The maximum query id in Q is denoted as maxId (Q).
also shares substantial computation across concurrent queries. We note that maxId (Q) ≥ |Q| in the general case, since we do not
Recent work [8, 18] has investigated work-sharing techniques for require query identifiers to be consecutive. Moreover, we expect
the computation of aggregates on chip multiprocessors. The devel- that maxId (Q) is bounded by a system parameter maxConc that
oped techniques essentially synchronize the execution of different limits the total number of concurrent queries.
aggregation operators in order to reduce contention on the hash ta- We use cij to denote the selection predicate placed by Qi on a di-
bles used for aggregate computation. As discussed later, C JOIN can mension table Dj that it references. We assume that cij ≡ TRUE
be combined with these techniques in an orthogonal fashion. if no explicit predicate is placed. We also define ci0 similarly with
Finally, work sharing has been investigated extensively in the respect to the fact table F . Finally, we use b to denote a bit-vector
context of streaming database systems [3, 6, 7, 14, 15, 16]. By shar- of bounded length, and b[l] to denote the l-th bit. The symbol 0
ing work (or state) among continuous-query operators, a streaming denotes the bit vector with all bits set to 0.
DBMS can maintain a low per-tuple processing cost and thus han- 3.1 Design Overview
dle a large number of continuous queries over fast streams. These
techniques are specific to streaming database systems and cannot C JOIN leverages the observation that star queries have a common
be applied directly to the environment that we target. An interest- structure: they “filter” the fact table through dimension predicates.
ing aspect of our proposed architecture is that it incorporates ele- Correspondingly, the architecture of C JOIN consists of a pipeline
ments from continuous query processing, which in turn allow us of components, as shown in Figure 1.
to transfer techniques from streaming databases to a DW setting.
Aggr.
For instance, C JOIN adopts the Grouped Filter operator of Mad- Continuous Scan Operator
den et al. [15], but extends it to support fact-to-dimension joins and Aggr.
Fact Operator
arbitrary selection predicates; the original operator only supported Table
Preprocessor Filter ... Filter Distributor
...
range predicates on ordered attributes. Aggr.
Operator
In summary, C JOIN enables a deeper form of work sharing than Pipeline
Manager
any prior work we know of: C JOIN employs a single plan that
shares I/O, join computation, and tuple storage across all C JOIN
queries that are in-flight at any given point in time. Figure 1: General architecture of the CJOIN pipeline.
Materialized Views. Materialized views enable explicit work shar-
ing by caching the results of sub-expressions that appear in concur- The C JOIN pipeline receives its input from a continuous scan of
rently executing queries. The selection of materialized views is the fact table and pipes its output to aggregation operators (either
typically performed off-line, by examining a representative work- sort-based or hash-based) that compute the query results. In be-
load and identifying common sub-expressions [10, 20]. Capturing tween, the fact tuples are processed through a sequence of Filters,
a representative workload is a challenging task in the context of ad- one for each dimension table, where each Filter encodes the cor-
hoc decision-support queries, due to the volatility of the data and responding dimension predicates of all queries in Q. In this way,
the diversity of queries. Moreover, materialized views add to the C JOIN can share I/O and computation among all queries in Q.
maintenance cost of the warehouse, and hence they do not offer The continuous scan implies that the operator is “always on,” i.e.,
clear advantages for the problem considered in this paper. a new query Q can be registered with the operator at any point in
time. The Preprocessor marks the point in the scan where Q enters
Constant Time Query Processing. BLINK [19] is a query pro- the operator and then signals the completion of Q when the scan
cessing architecture that achieves constant response time for the wraps around at that same point. This design turns the fact table
type of queries considered in our work. The idea is to run each into a “stream” that is filtered continuously by a dynamic set of
3](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-3-320.jpg)
![dimension predicates. only if the tuple is still relevant to at least one query), otherwise the
We illustrate the operation of the pipeline and the basic ideas be- tuple is discarded. In this example, the first Filter outputs a tuple τ
hind the design of C JOIN using the simple workload shown below: only if it joins with one of δ1 , δ2 , or δ3 . The second Filter forwards
′ ′
two star queries that join fact table F with dimension tables D1 and a fact tuple only if it joins with one of δ1 or δ2 . Since the two Fil-
D2 . The queries compute different aggregates and apply different ters work in sequence, τ appears in the output of the second Filter
selection predicates on D1 and D2 . only if its dimension values satisfy the predicates of Q1 or Q2 .
The Pipeline Manager regulates the operation of the pipeline.
SELECT Aggr 1 This component is responsible for registering new queries with
Q1 FROM F τ , D1 δ, D2 δ ′ C JOIN and for cleaning up after registered queries finish executing.
WHERE τ 1 δ 1 δ ′ AND σc11 (δ) AND σc12 (δ ′ ) Another important function is to monitor the performance of the
pipeline and to optimize it on-the-fly to maximize query through-
SELECT Aggr 2 put. For this reason and others that we mention below, it is desir-
Q2 FROM F τ , D1 δ, D2 δ ′ able for the Pipeline Manager to operate in parallel with the main
WHERE τ 1 δ 1 δ ′ AND σc21 (δ) AND σc22 (δ ′ ) pipeline. Therefore, this component has ideally its own execution
context (e.g., a separate thread or process).
Figure 2 shows a possible C JOIN pipeline for this workload. The Overall, the basic idea behind C JOIN is that fact tuples flow from
following paragraphs describe the functionality of each component the continuous scan to the aggregation operators, being filtered in
for this specific example. between based on the predicates of the dimension tables. At a high
level, this is similar to a conventional plan that would employ a
dim tuple bitvec
pipeline of hash join operators to join the fact table with the di-
Dimension mension tables. However, C JOIN shares the fact table scan among
1 10
Continuous fact tuple bitvec Hash Table
Scan 2 11 all queries, filters a fact tuple against all queries with a single di-
11
01
3 mension table probe, and stores the union of dimension tuples se-
Aggr1
Fact
lected by queries. Therefore, the fundamental difference from con-
Preprocessor Filter Filter Distributor ventional plans is that C JOIN evaluates all queries concurrently in
Table
Aggr2 a single plan that shares I/O, computation, and data. The pro-
posed design also differs from previous operator-centric designs
Pipeline dim tuple bitvec
'
Dimension (e.g., QPipe [11]) in that it takes advantage of the semantics of star
Manager 01 Hash Table
1 queries to provide a much tighter degree of integration and sharing.
' 11
2 For instance, QPipe would simulate two hash join operators with
different state for each query, whereas in our design there is only
one operator for all concurrent queries.
Figure 2: One possible instantiation of the CJOIN pipeline for
In this example we illustrated only one possible C JOIN pipeline
the example queries shown above.
for the sample workload. As we discuss later, there are other pos-
sibilities with potentially vast differences in performance. For in-
The Preprocessor receives tuples from the continuous scan and
stance, it is possible to change the order in which the Filters are
forwards them to the remainder of the pipeline. Each fact tuple τ is
applied. Another possibility is to have the Filter operators run in
augmented with a bit-vector bτ that contains one bit for each query
parallel using a variable degree of parallelism, e.g., the first Filter
in the workload. In this example, the bit-vector consists of two bits
can employ two parallel threads while the second Filter can have
such that bτ [1] = bτ [2] = 1. This signifies that, initially, every
just one thread. We discuss these issues in §3.4 and §4.
fact tuple is relevant for both queries Q1 and Q2 .
The Distributor receives fact tuples that are relevant for at least
one query in the current workload. Given a received fact tuple τ , 3.2 Query Processing
the Distributor examines its bit-vector bτ and routes it to the ag- We now discuss in more detail how the C JOIN operator evaluates
gregation operators of query Qi if and only if bτ [i] = 1. concurrent queries. For this part of our discussion, we assume that
A Dimension hash table stores a union of the tuples of a specific the workload Q remains fixed and that the operator uses a fixed
dimension table that satisfy the predicates of the current queries. In ordering of filters. We discuss later the admission of new queries
our example, say the predicates of Q1 select exactly two tuples δ1 (§3.3) and the optimization of the pipeline’s filter order (§3.4).
′
and δ2 from table D1 and one tuple δ2 from D2 , while Q2 selects
′ ′
tuples δ2 and δ3 from D1 and tuples δ1 and δ2 from D2 . Each
stored dimension tuple δ is augmented with a bit-vector bδ , whose 3.2.1 Dimension Hash Tables
length is equal to the bit-vector bτ attached to fact tuples, with the Each dimension table Dj referenced by at least one query is
following interpretation: bδ [i] = 1 iff the dimension tuple satisfies mapped to a hash table HD j , which stores those tuples of Dj that
the predicates of query Qi . For instance, the bit-vector for tuple are selected by at least one query in the workload. More formally,
δ1 is set as bδ1 [1] = 1 and bδ1 [2] = 0. Figure 2 illustrates the a tuple δ ∈ Dj is stored in HD j if and only if there exists a query
bit-vectors for all the tuples in our example. Qi that references Dj and δ satisfies cij . Tuple δ is also associ-
Each Filter retrieves fact tuples from its input queue and probes ated with a bit-vector bδ of length maxId (Q) that determines the
the corresponding dimension hash table to identify the joining di- queries that select δ. This bit-vector is defined as follows:
mension tuples. Given a fact tuple τ , the semantics of the foreign
key join ensure that there is exactly one dimension tuple δ that cor- 8
if there is no query Qi in Q
>0
responds to the foreign key value. If δ is present in the dimension >
>
hash table, then its bit-vector bδ is combined (using bitwise AND)
<1 if Qi references Dj ∧ δ satisfies cij
bδ [i] =
with the bit-vector bτ of τ . Otherwise, bτ is set to 0. The Filter >0
> if Qi references Dj ∧ δ does not satisfy cij
>
forwards τ to its output only if bτ = 0 after the combining (i.e., 1 if Qi does not reference Dj
:
4](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-4-320.jpg)
![The last case inserts an implicit TRUE predicate for a query Qi C JOIN Filtering Invariant Let Dd1 ,..., Ddm be the dimension ta-
that does not reference the dimension table. The reason is that Qi bles corresponding to the first m Filters in the C JOIN pipeline,
does not filter fact tuples based on Dj , so implicitly it selects all m ≥ 1. If a tuple τ appears in the output of the Filter corre-
the fact tuples in Dj . The hash table also records a single comple- sponding to Ddm , then we have bτ [i] = 1 if and only if Qi ∈ Q
mentary bitmap bDj defined as follows: bDj [i] = 1 if Qi does and τ satisfies the predicates of Qi on the fact table and τ joins
not reference Dj and bDj [i] = 0 otherwise. Essentially, bDj is with those dimension tuples in {Dd1 , . . . , Ddm } that also satisfy
the bitmap assigned to any tuple δ that does not satisfy any of the the predicates of Qi .
predicates in Q and hence is not stored in HD j . Tuple τ eventually reaches the Distributor if its bit-vector is non-
By definition, HD j stores only a subset of Dj . Each stored tuple zero after passing through all the Filters. Given that the Filters
is further augmented with a bit-vector of size maxId (Q), which cover all the dimension tables referenced in the current workload,
is a moderate memory overhead. Given that the dimension tables the invariant guarantees that bτ [i] = 1 if and only if τ satisfies all
tend to grow at a much slower rate than the fact table (typically, by
the selection and join predicates of Qi .
a logarithmic rate [17, 23]), it is reasonable to expect that the hash
The Distributor routes τ to the aggregation operator of each query
tables fit in main memory for modern hardware configurations. As Qi for which bτ [i] = 1. The aggregation operator can directly ex-
a concrete example, TPC-DS [23] employs 2.5GB of dimension tract any needed fact table attributes from τ . If the operator needs
data for a 1TB warehouse; today, even a workstation-class machine to access the attributes on some dimension Dj , then it can use the
can be economically equipped with 16GB of main memory. foreign key in τ to probe for the joining dimension tuple. A more
efficient alternative is to attach to τ memory pointers to the joining
3.2.2 Processing Fact Tuples dimension tuples as it is processed by the Filters. Specifically, let
We consider next the details of processing a fact tuple τ through δ be a tuple of Dj that joins to τ and assume that Qi references
the C JOIN pipeline, starting with the Preprocessor. The Preproces- Dj . Based on our definition of HD j , it is possible to show that δ is
sor attaches to τ a bit-vector bτ of length maxId (Q) that traces the in HD j when τ is processed through the corresponding Filter and
relevance of the tuple to different queries. This bit-vector is modi- remains in memory until τ reaches the Distributor. This makes it
fied as τ is processed by Filters and it is used in the Distributor to possible to attach to τ a pointer to δ after HD j is probed, so that the
route τ to aggregation operators. aggregation operator can directly access all the needed information.
The bit-vector is initialized based on the predicates placed on the
fact table, as follows: bτ [i] = 1 if Qi ∈ Qi ∧ τ satisfies ci0 (i.e., 3.2.3 Cost of C JOIN Query Processing
the selection predicate on the fact table) and bτ [i] = 0 otherwise. The design of C JOIN has specific implications on the cost of
After bτ is initialized, the Preprocessor forwards it to its output query processing, which we discuss below.
queue if bτ = 0. In the opposite case, τ can be safely dropped We consider first the end-to-end processing for a single fact tuple
from further processing, as it is guaranteed to not belong to the through the C JOIN operator. Once a tuple is initialized in the Pre-
output of any query in Q. Computing bτ involves evaluating a set processor, if K is the total number of Filters in the pipeline, then
of predicates on τ , and thus it is necessary to employ an efficient processing the fact tuple involves K probes and K bit-vector AND
evaluation mechanism to ensure that the Preprocessor does not be- operations in the worst case. Since the probe and the AND opera-
come the bottleneck. This issue, however, is less crucial in practice, tion have limited complexity, and assuming that the Preprocessor
since most queries place predicates solely on dimension tables. can initialize efficiently the bit-vector of the tuple, C JOIN can sus-
Tuple τ passes next through the sequence of Filters. Consider tain a high throughput between the continuous scan and the aggre-
one such filter, corresponding to dimension table Dj . Let δ be the gation operators. Moreover, the reliance on sequential scans as the
joining dimension tuple for τ . The Filter probes HD j using the sole access method allows C JOIN to scale gracefully to large data
foreign key of τ and eventually computes (as explained in the next sets, without incurring the costs of creating and maintaining mate-
paragraph) a “filtering bit-vector” denoted by bτ 1HD j , which re- rialized views or indices on the fact table, or maintaining statistics.
flects the subset of queries that select δ through their dimension We discuss now the cost of a single query. The response time of
predicates. The Filter thus joins τ with Dj with respect to all a query evaluated with C JOIN is dominated by the time required to
queries in the workload by performing a single probe to HD j . Sub- loop around the continuous scan. This cost is relatively stable with
sequently, bτ is bitwise ANDed with bτ 1HD j . If this updated bτ respect to the total number of queries in the workload, because the
vector is 0, then the fact tuple can safely be dropped from further I/O is shared across all queries and the cost of probing in each Fil-
processing, since it will not belong to the output of any query in Q; ter (cost of a hash table lookup and cost of a bitwise AND) grows
otherwise it is passed to the output of the Filter. As an optimization, at a low rate with the number of queries. Thus, as long as the rate
it is possible to avoid completely the probing of HD j by checking of query submission does not surpass the rate of query completion,
first whether bτ AND ¬bDj is 0 (i.e., Dj does not appear in any C JOIN yields response times with low variance across different de-
query Qi to which τ is relevant). In this case, τ is not relevant to grees of concurrency. This property is crucial if we are to scale
any queries that reference HD j and can be simply forwarded to the effectively to a large number of concurrent queries.
next Filter. An added bonus is that the current point in the continuous scan
The filtering bit-vector is computed as follows: if the probe finds can serve as a reliable progress indicator for the registered queries,
δ in HD j then bτ 1HD j = bδ , similar to the example of Figure 2; and it is also possible to derive an estimated time of completion
otherwise, bτ 1HD j is set to bDj , the bit-vector of any tuple that based on the current processing rate of the pipeline. Both of these
is not stored in HD j . Given the definitions of bδ and bDj , we metrics can provide valuable feedback to users during the execution
can assert the following key property for the filtering bit-vector: of ad-hoc analytic queries in large data warehouses.
bτ 1HD j [i] = 1 if and only if either Qi references Dj and δ is The predictability property implies that query response time is
selected by Qi , or Qi does not reference table Dj . This property bounded below by the cost of a full sequential scan of the fact ta-
ensures that bτ AND bτ 1HD j results in a bit-vector that reflects ble. Conventional physical plans for star queries are likely to have
accurately the relevance of τ to workload queries up to this point. the same property; for instance, a common plan in commercial sys-
This can be stated formally with the following invariant: tems is a left-deep pipeline of hash joins with the fact table as the
5](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-5-320.jpg)
![outer relation. In principle, the large table scan can be avoided Algorithm 1: Admitting a new query to the C JOIN pipeline.
by the use of indices or materialized views, but these structures Input: Query Qn
are generally considered too expensive in the DW setting, because Data: A list L of dimension hash tables, initially empty
fact table indices have a prohibitively high maintenance cost, and 1 Let D be the set of dimension tables referenced by Qn
ad-hoc data analysis workloads may not be stable enough to iden- 2 Let D ′ be the set of dimension tables in the pipeline
tify useful views to materialize. A common method in practice is 3 foreach Dj ∈ D ∪ D ′ do
to limit queries on specific partitions of the fact table; as will be 4 if Dj is not in the pipeline then
5 Initialize HD j and bDj based on Q ∪ {Qn }
discussed in §6, this method can also be integrated in C JOIN with
6 Append HD j to L
similar benefits. In any case, we stress that C JOIN becomes yet one
7 else if Dj is referenced by Qn then
more choice for the database query optimizer; it is always possi- 8 bDj [n] = 0
ble to execute queries with conventional execution plans if this is 9 else
estimated to be more efficient. 10 bDj [n] = 1
3.3 Query Admission and Finalization 11 foreach Dj ∈ D do
12 foreach δ ∈ σcnj (Dj ) do
Up to this point, we have examined the processing of fact tu- 13 if δ is not in HD j then
ples assuming that the C JOIN pipeline has been initialized correctly 14 Insert δ in HD j
with respect to a given workload. In this section, we discuss how 15 bδ ← bDj
the state of the C JOIN pipeline is updated when a new query is ad- 16 bδ [n] ← 1;
mitted, or when an existing query finishes its processing.
We use n to denote the id of the query in question. For a new 17 Stall Preprocessor;
query, n is assigned as the first unused query id in the interval 18 foreach HD j in L do insert a Filter for HD j
19 Q ← Q ∪ {Qn };
[1, maxConc], where maxConc is the system-wide limit on the
20 Set start of Qn to next tuple in Preprocessor’s input
maximum number of concurrent queries. To simplify our presenta- 21 Append a control tuple τQn in Preprocessor’s output
tion, we assume without loss of generality that n ≤ maxId (Q). 22 Resume Preprocessor
3.3.1 Admitting New Queries
The registration of Qn is done through the Pipeline Manager,
which orchestrates the update of information in the remaining com- will not miss any relevant fact tuples.
ponents. This approach takes advantage of the fact that the Pipeline It is important to note that query registration occurs in the Pipeline
Manager executes in parallel with the C JOIN pipeline, thus mini- Manager thread and thus it can proceed, up to line 17, in parallel
mizing the disruption in the processing of fact tuples. with the processing of fact tuples through the pipeline. This ensures
The registration is performed in the Pipeline Manager thread us- that other queries are minimally disrupted during the registration of
ing Algorithm 1. The first step is to update bit n of bDj for each Qn . The concurrent update of the bit-vectors in dimension hash ta-
dimension table that is referenced by Qi or appears in the pipeline bles does not compromise the correctness of results, since the Pre-
(line 3). Subsequently, the algorithm updates the hash tables for processor continues to mark each fact tuple as irrelevant to query
the dimensions referenced in the query (line 11). For each such di- Qn (bτ [n] = 0). Thus, even if bδ [n] is switched on for some tuple
mension table Dj , the Pipeline Manager issues the query σcnj (Dj ) δ (line 16), it does not lead to the generation of results for Qn until
and updates HD j with the retrieved dimension tuples. If a retrieved after it becomes part of the workload in line 19, because bit n in
tuple δ is not already in HD j , then δ is inserted in HD j and its bit- the fact tuples’ bit-vectors will be 0 until that point.
vector initialized to bDj . We then set bδ [n] ← 1 to indicate that δ
is of interest to Qn . At the end of these updates, all the dimension 3.3.2 Finalizing Queries
hash tables are up to date with respect to the workload Q ∪ {Qn }. Query Qn is finalized when the continuous scan wraps around
Having updated the dimension tables, the algorithm completes the starting fact tuple τ . Upon encountering τ in its input, the Pre-
the registration by installing Qn in the Preprocessor and the Dis- processor first removes Qn from Q, which ensures that the bit-
tributor. This involves several steps. First, the Pipeline Manager vector of τ (and of any subsequent tuple) will have bit n switched
suspends the processing of input tuples in the Preprocessor, which off. This ensures that Qn becomes irrelevant for the filtering of
stalls the pipeline (line 17). This enables the addition of new Fil- fact tuples. Subsequently, the Preprocessor emits an “end of query”
ters in the pipeline to cover the dimension tables referenced by the control tuple that precedes τ in the output stream. The control tu-
query. (While new Filters are appended in the current pipeline, ple is handled in a fashion similar to the query-start tuple and is
their placement may change as part of the run-time optimization— forwarded through the pipeline to the Distributor, which finalizes
see §3.4.) Q is also updated to include Qn , which allows bit n of the aggregation operators of Qn and outputs their results. Since the
the fact tuple bit-vector to be initialized correctly. Next, the first control tuple precedes τ , we ensure that the aggregation operators
unprocessed input fact tuple, say τ , is marked as the first tuple of of Qn will not consume any fact tuple more than once.
Qn , so that it is possible to identify the end of processing Qn (see The final step is to clear the dimension hash tables from any in-
next paragraph). Finally, a special “query start” control tuple τn formation pertinent to Qn . This is handled in the Pipeline Man-
that contains Qn is appended to the output queue of the Preproces- ager thread according to Algorithm 2, which essentially reverses
sor, and the Preprocessor is resumed. The control tuple precedes the updates performed when the query was admitted. This clean-
the starting tuple τ in the output stream of the Preprocessor and is up may render certain information in the hash tables useless. For
forwarded without filtering through the Filters and on to the Dis- instance, if for some tuple δ in HD j we have δ[i] = 0, then δ can
tributor. In turn, the latter uses the information in τQn to set up the be removed. In turn, if HD j becomes empty, then it can be re-
aggregation operators for Qn . Since τQn precedes any potential moved from the pipeline along with the corresponding Filter. Of
results for Qn (the pipeline preserves the order of control tuples course, the latter requires a stall of the pipeline in order to recon-
relative to data tuples), we guarantee that the aggregation operators figure the Filter sequence. Note that this “garbage collection” can
6](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-6-320.jpg)
![Algorithm 2: Removing a finished query from the pipeline. imizes the expected processing cost of each stream tuple. The cor-
Input: Query Qn . respondence to C JOIN appears when viewing Filters as predicates,
Data: A list L of dimension hash tables, initially empty. and the continuous scan as an infinite stream. Moreover, since each
1 Let D be the set of dimension tables referenced by Qn ; Filter has a fixed cost—one probe of the in-memory hash table
2 Let D ′ be the set of dimension tables in the pipeline ; and one bitwise AND operation—minimizing the expected process-
3 foreach Dj ∈ D ′ do ing cost is equivalent to minimizing the expected number of Filter
4 bDj [n] = 1; probes. In our work, we employ the techniques of Babu et al. [5]
5 foreach Dj ∈ D do to implement the run-time optimization of the Filter ordering. A
6 foreach δ ∈ HD j do detailed discussion of these techniques is beyond the scope of our
7 bδ [n] ← 0; paper. We do note, however, that other techniques are applicable
8 if bδ = 0 then remove δ from HD j
too, such as those introduced by Liu et al. [13].
9 if HD j = ∅ then Append HD j to L
10 if L = ∅ then 3.5 Handling Updates
11 Stall pipeline; Up to this point, we have considered the case of read-only trans-
12 foreach HD j ∈ L do remove corresponding Filter;
actions that reference the same data snapshot. This enables group-
13 Resume pipeline;
ing all queries of these transactions in the same C JOIN operator
that performs a single continuous scan of the specific snapshot.
In the remainder of this section we examine adaptations of C JOIN
be done asynchronously (as long as the query identifiers are cor- when this assumption is relaxed, i.e., when the queries correspond
rectly handled); one could also maintain usage bits and evict the to transactions with different snapshot ids. (As mentioned in §2,
least-recently-used tuples according to memory needs. we assume snapshot-based isolation, since this is the norm in prac-
tice.) This scenario arises when read-only transactions are inter-
3.3.3 Correctness leaved with updates, or when the same transaction contains both
The correctness of C JOIN with respect to query finalization hinges queries and updates. In all cases that we examine, we focus on up-
upon two properties. First, the continuous scan returns fact tuples in dates that reference only the fact table. In the rare event of updates
the same order once resumed. This is necessary so that the Prepro- on dimension tables, we assume that the admission of new queries
cessor can identify correctly when the fact table has been scanned in C JOIN is serialized with the transaction of the update.
exactly once for each query. It is reasonable to expect that this prop- We consider two possibilities for adapting C JOIN to this sce-
erty holds for real-world systems. The second property is that, if a nario, that depend on the functionality of the continuous scan op-
control tuple τ ′ is placed in the output queue of the Preprocessor erator. The first possibility is that the continuous scan operator can
before (respectively after) a fact tuple τ , then τ ′ is not processed in return all fact tuples corresponding to the snapshots in the current
the Distributor after (respectively before) τ . This property guaran- query mix. This essentially requires the scan to expose the multi-
tees that the aggregation operators of a query neither miss relevant version concurrency control information for the retrieved fact tu-
tuples nor process them more than once. This property needs to be ples. Then, the association of a query Qi to a specific snapshot can
enforced by the implementation of the C JOIN pipeline. be viewed as a virtual fact table predicate, and it can be evaluated by
the Preprocessor over the concurrency control information of each
3.4 Pipeline Optimization fact tuple. The remaining C JOIN mechanism remains unchanged.
Of course, the benefits of the C JOIN operator are decreased as the
The order of Filters in the pipeline influences performance, be-
snapshots referenced by the transactions become disjoint, but we
cause it determines the expected number of probes for each fact
believe this case to be infrequent in practice.
tuple. Drawing a correspondence to the ordering of joins in a sin-
The second possibility is when the previous functionality is not
gle query plan, we expect that a good order will apply the most
provided, i.e., the scan only returns tuples of a specific snapshot. In
selective Filters first, in order to drop fact tuples early. We there-
this case, we create several C JOIN operators, one for each snapshot
fore face the following optimization problem: Given a workload Q
that is referenced, and register queries to the respective operator.
and a C JOIN pipeline for Q, determine an ordering of the Filters
This approach could degenerate into a single plan per query, if each
that minimizes the expected number of probes for each fact tuple.
transaction in our workload mix referenced different snapshot ids.
One complicating factor is that the selectivity of each Filter de-
This, however, is an exceptionally rare event in practice.
pends on the workload Q, since a Filter encodes the join predicates
of several queries on a specific dimension table. Thus, if the work-
load is unpredictable, as is the case with ad-hoc analytics in a data 4. CJOIN IMPLEMENTATION
warehouse, then the optimal order might change as the query mix In this section, we discuss the implementation of C JOIN on a
changes. This observation suggests an online approach to optimiz- multi-core system, the predominant hardware architecture in real-
ing the order of Filters in the C JOIN pipeline. The idea is to monitor world deployments today and in the near future. Nevertheless, we
at run-time the selectivity of each Filter and then optimize the order expect C JOIN to yield significant benefits on single-core/single-
based on the gathered statistics. This continuous process of mon- CPU hardware as well.
itoring and re-optimizing can be performed asynchronously inside An efficient implementation of C JOIN on a multi-core architec-
the Pipeline Manager thread. ture requires that the operator’s components (Preprocessor, Filters,
Previous work introduced several techniques for optimizing the and Distributor) be mapped to multiple threads, which in turn are
execution order of relational operators on-the-fly [4, 5, 13]. In par- mapped by an operating system to different processor cores. As an
ticular, the optimization of the C JOIN pipeline maps precisely to example, one obvious mapping is to assign each component to a
the following problem that has been investigated in the context of different thread and then employ tuple queues to link the pipeline.
streaming database systems: We are given a conjunction of pred- However, the mapping of C JOIN components to threads must strike
icates that are applied on the tuples of an infinite stream, and the a balance between the degree of parallelism, the overhead of pass-
goal is to determine an order for evaluating the predicates that min- ing tuples between the threads, and the utilization of processor
7](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-7-320.jpg)
![caches. Passing a tuple from one thread to another requires syn- thread retrieve or deposit tuples in batches, whenever possible. Fi-
chronization between the threads and also results in data cache nally, we reduce the cost of memory management synchronization
misses if the two threads execute on different cores. On the other by using a specialized allocator for fact tuples. The specialized al-
hand, executing components in different threads improves cache locator preallocates data structures for all in-flight tuples, whose
locality if the internal state is read-mostly (such as the dimension number is determined based on the upper bound on the length of a
hash tables) and can be partitioned among multiple threads. tuple queue and the upper bound on the number of threads. Given
Since the internal states of the Preprocessor and Distributor are the pool of preallocated tuples, the allocator reserves and releases
frequently updated, we chose to map each to a single thread as tuples using bitmap operations, which entail a single machine in-
shown in Figure 3. Filters, where the bulk of C JOIN processing struction on most CPUs, thus being both atomic and efficient.
happens, do not have any internal state other than the dimension
hash tables, which are read-mostly. Our implementation allows for
a flexible mapping of Filters to threads by collapsing multiple ad-
5. EXTENSIONS
jacent Filters to a Stage (to reduce the overhead of passing tuples In this section, we revisit some of the assumptions made in §2.
between the threads) and assigning multiple threads to each Stage We discuss ways in which C JOIN can be adapted to accommodate
(to increase parallelism). This approach gives rise to the following the lifting of these assumptions.
possible configurations: Galaxy Schemata. A galaxy schema involves several fact rela-
• A vertical configuration assigns a single Stage to each Filter, with tions, each of which is the center of a star schema. Star queries
a (potentially) different number of threads per Stage. This design remain common in this setting and can thus be evaluated using
favors the affinity of Stages to cores so that instruction and data C JOIN, but it is also common to observe queries involving the join
locality is maximized. On the other hand, we expect a large number of several fact tables (typically two).
of data cache misses when tuples are transferred between Filters. C JOIN can benefit the evaluation of these queries even though
Moreover, the problem of pipeline optimization now acquires an it was not designed for this specific case. Concretely, consider a
extra free variable: the number of threads per Stage. query Q with a single fact-to-fact join predicate. By using the fact-
to-fact join as a pivot, we can express the evaluation of Q as the
• A horizontal configuration assigns a single Stage to the entire join between the results of two star queries, say Qa and Qb , over
sequence of Filters, and all the threads are assigned to this single the corresponding fact tables. It now becomes possible to register
Stage. This implies that several copies of the Filter sequence are each Qi with the C JOIN operator that handles the concurrent star
running in parallel (one for each thread) and accessing the same queries on the corresponding fact table, the difference being that
hash tables. This scheme avoids data cache misses when tuples are the Distributor pipes the results of Qi to a fact-to-fact join operator
passed between Filters, but may incur more misses on the accesses instead of an aggregation operator. Notice that each C JOIN operator
of the hash tables, since each thread needs to access more data. will be evaluating concurrently several star queries that participate
Pipeline optimization involves solely ordering the Filters. in concurrent fact-to-fact join queries. Thus, the overall idea is to
• A hybrid configuration employs several Stages and an assign- use C JOIN as a physical operator that can evaluate efficiently the
ment of threads per Stage. This configuration can strike a balance “star sub-plans” of bigger query plans.
between the two extremes of a horizontal vs. vertical configuration. Column Stores. Column stores have been gaining traction as a
More concretely, the cost of tuple passing is incurred only between scalable system architecture for large data warehouses [1, 2, 22]. It
Stages, and each thread needs to access solely the dimension ta- is possible to adapt C JOIN in this setting as follows: The continuous
bles that exist within a Stage. However, the run-time optimization fact table scan can be realized with a continuous scan/merge of only
becomes more complex, as there are now three free variables: the those fact table columns that are accessed by the current query mix.
order of Filters, the boxing of Filters in Stages, and the assignment Thus, C JOIN can take advantage of the columnar store in order
of threads to Stages. to reduce the volume of data transferred by the scan. The other
Stage Stage case that we need to examine is the evaluation of filter queries over
dimension tables, which occurs as part of a new query registration.
This case is readily handled by the column store, since C JOIN uses
the existing query processing infrastructure to retrieve the resulting
dimension tuples.
Preprocessor Filter Filter Filter Filter Filter Distributor
Compressed Tables. Data warehouses may employ compression
to reduce the amount of I/O and memory bandwidth used for data
transfer [1, 19]. C JOIN makes no assumptions about the physi-
Figure 3: An example mapping of a CJOIN pipeline to threads. cal storage of tuples, except that it is possible to evaluate predi-
cates, extract fields, and retrieve result tuples for dimension queries.
Thus, compression of tables is an orthogonal technique that can be
Our experiments indicate that the extra parallelism resulting from
using multiple Stages does not outweigh the cost of forwarding the easily incorporated in C JOIN. For instance, the continuous scan
tuples between them. Consequently, we henceforth assume the hor- can bring in compressed tuples and decompress on-demand and on-
izontal configuration, and we achieve parallelism by allocating sev- the-fly as needed for probing the dimension hash tables. Another
option is to use the partial decompression technique proposed in
eral threads to the single Stage.
BLINK [19] in order to evaluate predicates efficiently on the com-
A few well-known design principles turned out to be crucial to
achieving good C JOIN performance in our prototype. To reduce pressed fact table.
the overhead of thread scheduling, we wake up a consumer thread Fact Table Partitioning. The organization of the fact table in parti-
only when its input queue is almost full. Similarly, we resume the tions may arise naturally from the operational semantics of the DW,
producer thread only when its output queue is almost empty. We e.g., the fact table may be range-partitioned by a date attribute cor-
also reduce the overhead of queue synchronization by having each responding to the loading of new data. The optimizer can take ad-
8](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-8-320.jpg)
![vantage of this partitioning in order to limit the execution of a query 6.1.1 Systems
to a subset of the fact table. Thus, a query that sets a range pred- Our C JOIN prototype is implemented as a multi-threaded pro-
icate on the partitioning date attribute will need to examine only a cess executing on top of the PostgreSQL database system. C JOIN
subset of the partitions. In principle, this approach can reduce sig- uses PostgreSQL to issue queries over the dimension tables for the
nificantly the response time of an individual query, but concurrent registration of new queries. The continuous scan is implemented
queries can still lead to random I/O, which has crippling effects on by issuing successive SELECT * FROM F queries to PostgreSQL.
overall performance. To increase the throughput of the scan, we have implemented a
C JOIN can take advantage of partitioning in order to reduce the fast tuple copy mechanism between PostgreSQL and C JOIN using
volume of data accessed by the continuous scan and also to reduce a shared memory buffer. Our prototype supports both the horizontal
query response time. More concretely, the query registration algo- (one Stage for all Filters) and vertical (one Stage per Filter) config-
rithm can be modified to tag each new query with the set of parti- urations described in §4.
tions that it needs to scan. This set can be determined by correlating We compare C JOIN to both a widely used commercial database
the selection predicates on the fact table with the specific partition- system (henceforth referred to as “System X”) and PostgreSQL. We
ing scheme. The Preprocessor can then realize the continuous scan tune both systems (e.g., computation of optimization statistics, al-
as a sequential scan of the union of identified partitions. At the end lowing a high number of concurrent connections, scans using large
of each partition, the end-of-query control tuple can be emitted for data chunks, etc.) to ensure that the experimental workloads are
the queries that have covered their respective set of partitions, thus executed without obvious performance problems. We have veri-
allowing queries to terminate early. fied that both systems employ the same physical plan structure to
Efficient Aggregate Computation. The current C JOIN design for- evaluate the star queries in the experimental workloads, namely, a
wards the resulting tuples to aggregation operators that compute pipeline of hash joins that filter a single scan of the fact table. The
the final query results. There may be opportunities to optimize this small size of the dimension tables implies that they can be cached
final stage, e.g., by sharing work among aggregation operators, de- efficiently in main memory and hence their processing is expected
pending on the current query mix. This optimization is orthogonal to be very fast. As a result, we do not tune the physical design of
to C JOIN and can be performed using existing techniques [8, 18]. any of the database systems with indices or materialized views on
the dimension tables, since this would not improve query response
Memory-resident Databases. The design of C JOIN was motivated time (we verified this claim for the experimental workloads). We
by large-scale data warehouses, where the fact table is orders of also avoid using indices and views on the fact table, for the obvi-
magnitude larger that the available main memory. However, it is ous reasons mentioned in previous sections. For PostgreSQL, we
straightforward to employ C JOIN for a memory-resident data set as enable the shared-scans feature to maximize its work sharing.
well. One difference is that the sharing of the continuous scan may Our experimental server has two quad-core Intel Xeon CPUs,
not have as significant an effect as when the fact table resides on with a unified 6 MB L2 cache on each CPU shared among all 4
disk. Still, C JOIN will enable work sharing among the concurrent cores and 8 GB of shared RAM. The machine has four HP 300GB
queries, which is important in achieving high throughput. 15K SAS disks, arranged in a hardware-controlled RAID-5 array.
Indexes and Materialized Views. As discussed earlier, fact table
indexes are not likely to be useful in the DW setting that we con- 6.1.2 Data Set and Workload
sider, due to their high maintenance cost. Similarly, the inherent We employ the data set and queries defined in the Star Schema
volatility of ad-hoc queries limits the appearance of common pat- Benchmark (SSB) [17]. We choose this particular benchmark be-
terns and hence the importance of materialized views that involve cause it models a realistic DW scenario and targets exactly the class
the fact table. It is more common (and affordable) for data ware- of queries that we consider in our work.
houses to maintain indexes and views on dimension tables. C JOIN We generate instances of the SSB data set using the data genera-
takes advantage of these structures transparently, since they can op- tor supplied with the benchmark. The size of each instance is con-
timize the dimension filter queries that are part of new query regis- trolled by a scale factor parameter denoted as sf . A value sf = X
tration (see also Algorithm 1). results in a data set of size X GB, with 94% of the data correspond-
ing to the fact table. We limit the maximum value of the scale factor
6. EVALUATION to 100 (i.e., a 100GB data set) to ensure the timely execution of the
This section reports the results of an experimental evaluation of test workloads on our single experimental machine.
our C JOIN prototype. We investigate the performance characteris- We generate workloads of star queries from the queries speci-
tics of C JOIN and compare it to real-world database systems using fied in the benchmark. Specifically, we first convert each bench-
workloads of different characteristics. In particular, we focus on mark query to a template, by substituting each range predicate in
the following high-level questions: the query with an abstract range predicate, e.g., d_year >= 1992
and d_year <= 1997 is converted to d_year >= X and d_year
• Which is the best way to map the components of a C JOIN pipeline <= Y, where X and Y are variables. To create a workload query, we
to CPUs? (§6.2.1) first sample a query template and then substitute the abstract ranges
• How does C JOIN throughput scale with increasing numbers of with concrete predicates based on a parameter s that controls the se-
concurrent queries? (§6.2.2) lectivity of the predicate. Thus, s allows us to control the number
• How sensitive is the throughput of C JOIN to workload character- of dimension tuples that are loaded by C JOIN per query, as well as
istics? (§6.2.3) the size of the hash tables in the physical plans of PostgreSQL and
• How does the size of a data warehouse impact C JOIN’s perfor- System X.
mance? (§6.2.4) Note that the original benchmark specification contains 13 queries
of varying complexity. We excluded queries Q1.1, Q1.2 and Q1.3
6.1 Methodology from the generation of workload queries because they contain se-
We describe here the systems, data sets, workloads, and evalua- lection predicates on fact table attributes, and this functionality is
tion metrics that characterize our experiments. not yet supported by our prototype. This modification does not af-
9](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-9-320.jpg)
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12](https://image.slidesharecdn.com/cjoin-100107202317-phpapp01/85/Cjoin-12-320.jpg)
Cjoin
- 1. Appears in Proceedings of the 35th International Conference on Very Large Data Bases (VLDB), Lyon, France (August 2009) A Scalable, Predictable Join Operator for Highly Concurrent Data Warehouses George Candea Neoklis Polyzotis Radek Vingralek EPFL & Aster Data Systems U.C. Santa Cruz Aster Data Systems george.candea@epfl.ch alkis@ucsc.edu radek.vingralek@asterdata.com ABSTRACT increase query latency. For example, one of our large DW clients Conventional data warehouses employ the query-at-a-time model, specifically asked that increasing concurrency from one query to 40 which maps each query to a distinct physical plan. When several should not increase latency of any given query by more than a fac- queries execute concurrently, this model introduces contention, be- tor of six. Large organizations employing DWs indicate that their cause the physical plans—unaware of each other—compete for ac- data warehouses will have to routinely support many hundreds of cess to the underlying I/O and computation resources. As a result, concurrent queries in the near future. while modern systems can efficiently optimize and evaluate a single We know of no general-purpose DW system that can meet these complex data analysis query, their performance suffers significantly real-world requirements today. Adding a new query can have un- when multiple complex queries run at the same time. predictable effects or predictably negative ones. For instance, when We describe an augmentation of traditional query engines that going from 1 to 256 concurrent queries, the query response time in improves join throughput in large-scale concurrent data warehouses. a widely used commercial DBMS increases by an order of mag- In contrast to the conventional query-at-a-time model, our approach nitude; in open-source PostgreSQL, it increases by two orders of employs a single physical plan that can share I/O, computation, and magnitude. Queries that take hours or days to complete are no tuple storage across all in-flight join queries. We use an “always- longer able to provide real-time analysis, since, depending on isola- on” pipeline of non-blocking operators, coupled with a controller tion level, they may need to operate on hours-old or days-old data. that continuously examines the current query mix and performs This situation leads to “workload fear”: users of the DW are pro- run-time optimizations. Our design allows the query engine to scale hibited from submitting ad-hoc queries and only sanctioned reports gracefully to large data sets, provide predictable execution times, can be executed. In order to achieve better scalability, organizations and reduce contention. In our empirical evaluation, we found that break their data warehouse into smaller data marts, perform aggres- our prototype outperforms conventional commercial systems by an sive summarization, and batch query tasks. These measures, how- order of magnitude for tens to hundreds of concurrent queries. ever, delay the availability of answers, restrict severely the types of queries that can be run (and consequently the richness of the in- formation that can be extracted), and increase maintenance costs. 1. INTRODUCTION In effect, the available data and computation resources end up be- Businesses and governments rely heavily on data warehouses to ing used inefficiently, preventing the organization from taking full store and analyze vast amounts of data; the information within is advantage of their investment. Workload fear acts as a barrier to key to making sound strategic decisions. Data warehousing has re- deploying novel applications that use the data in imaginative ways. cently penetrated the domains of Internet services, social networks, This phenomenon is not necessarily due to faulty designs, but advertising, and product recommendation, where complex queries merely indicates that most existing DBMSes were designed for are used to identify behavioral patterns in users’ online activities. a common case that is no longer common—workloads and data These systems query ever increasing volumes of data—hundreds volumes, as well as hardware architectures, have changed rapidly of terabytes to petabytes—and the owners of the data scramble to in the past decade. Conventional DBMSes employ the query-at- “monetize” it, i.e., distill the data into social or financial profit. a-time model, where each query is mapped to a distinct physi- Unlike in the past, modern data warehouse (DW) deployments cal plan. This model introduces contention when several queries require support for many concurrent users. Commercial customers execute concurrently, as the physical plans compete in mutually- today require support for tens of concurrent queries, with some unaware fashion for access to the underlying I/O and computation even wishing to concurrently process hundreds of reports for the resources. As a result, concurrent queries result in random I/O; same time period. Moreover, such customers desire that going for a 1-petabyte DW, even a query that touches only 0.1% of the from one query to several concurrent ones should not drastically database will still retrieve on the order of 100GB of data, thus likely performing a crippling number of random I/O operations. Contributions. This paper introduces a query processing architec- Permission to copy without fee all or part of this material is granted provided ture that enables DW systems to scale to hundreds of concurrent that the copies are not made or distributed for direct commercial advantage, users, issuing ad-hoc queries and receiving real-time answers. Our the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data goal is to enable a new way of using data warehouses, in which Base Endowment. To copy otherwise, or to republish, to post on servers users shed their workload fear and experiment freely with ad-hoc or to redistribute to lists, requires a fee and/or special permission from the data analysis, drill arbitrarily deep, and broaden their queries. publisher, ACM. VLDB ’09, August 24-28, 2009, Lyon, France More concretely, we introduce C JOIN, a physical operator that Copyright 2009 VLDB Endowment, ACM 000-0-00000-000-0/00/00. can evaluate concurrent join queries efficiently. The design of C JOIN
- 2. achieves deep sharing of both computation and resources, and it is fact-to-dimension joins and selection predicates. A join predicate well suited to the characteristics of modern DW platforms: star F 1 Ddj has the standard form of a key/foreign-key equi-join. A schema design, many-core systems, fast sequential scans, and large selection predicate cj can be arbitrarily complex (e.g., contain dis- main memories. Using C JOIN as the basis, we build a query pro- junction or sub-queries), but can reference solely the tuple variable cessing engine that scales gracefully to highly concurrent, dynamic of Ddj from the star query. For convenience of notation, we set cj workloads. The query engine employs a single physical plan that to TRUE if the query does not place a predicate on the correspond- is “always on” and is optimized continuously based on run-time ing table. Note that we allow for the case where B = ∅ (i.e., there statistics. A new query can latch onto the single plan at any point is no GROUP BY clause, so either k = 0 or A = ∅) or A = ∅. in time, and it immediately starts sharing work with concurrent In the remainder of the paper, we assume the most general case, queries in the same plan. This deep, aggressive sharing is key to where A = ∅, B = ∅, and k > 0. C JOIN’s efficiency and sets it apart from prior work. Problem Statement. We consider the problem of efficiently eval- Measurements indicate that C JOIN achieves substantial improve- uating a large number of concurrent star queries in a single data ment over state-of-the-art commercial and research systems. For warehouse. These queries can either be submitted directly by users, 256 concurrent queries on a star schema, C JOIN outperforms ma- or constitute sub-plans of more complex queries. jor commercial and open-source systems by a factor of 10 to 100 An effective solution to this problem should yield high query on the Star Schema Benchmark [17]. For 32 concurrent queries, throughput, as well as enable graceful degradation of query re- C JOIN outperforms them by up to 5x. More importantly, when sponse time as the number of concurrent queries increases (i.e., going from 1 to 256 concurrent queries, C JOIN’s response time in- avoid thrashing). This goal also implies a notion of predictability: creases by less than 30%, compared to over 500% for a leading Query response time should be determined primarily by the char- commercial system. acteristics of the query, and not by the presence or absence of other The rest of the paper is structured as follows: §2 describes our queries executing concurrently in the system. Existing general- target data warehousing setting and summarizes related work; §3 purpose DWs do not fare well in this setting, hence our motivation details the C JOIN operator and the new query processing engine to find a solution suitable for highly concurrent data warehouses. built around it; §4 describes the deployment of C JOIN on modern We emphasize that the overall workload need not be restricted DW platforms; §5 presents several extensions; §6 evaluates various solely to star queries. On the contrary, we envision a system archi- aspects of performance and scalability; and §7 concludes. tecture where concurrent star queries are diverted to a specialized query processor (such as the one presented in this paper) and any 2. BACKGROUND AND STATE OF THE ART other SQL queries and update statements are handled using conven- In this section, we provide background on the central problem tional infrastructure. While it is clearly desirable to support high addressed in our paper: improving support for concurrent queries concurrency across all types of queries, there are significant chal- in large data warehouses (§2.1). We then survey related work that lenges even in doing so for just the subset of star queries. Moreover, has approached this or similar challenges (§2.2). this focus does not restrict the practicality of our solution, since star queries are common in DW workloads. Finally, our query evalua- 2.1 Our Target Domain tion techniques can be employed as sub-plans, to evaluate the star Data Warehousing Model. Below, we describe the model targeted “portion” of more complex queries. by our solution; in §5 we show how specific assumptions behind Physical Data Storage. We develop our techniques assuming that this model can be lifted without affecting our techniques. the DW employs a conventional row-store for data storage. This as- We consider a DW that organizes information using a star schema, sumption is driven by the design of existing commercial DW solu- which has become standard in the data warehousing industry. We tions, including Oracle, IBM, Microsoft, Teradata, and the product assume a fact table F that is linked through foreign keys to d di- within which C JOIN was developed. However, our approach can mension tables D1 , . . . , Dd . Following common practice, we as- be applied equally well to different architectures. For instance, it sume that F is too large to fit in main memory and is considerably is possible to implement C JOIN within a column store or a system larger than the dimension tables. employing compressed tables. We examine these cases in §5. The warehouse supports a workload of SQL queries, including We do not make any specific assumptions about the physical de- periodic updates. Following common industrial practice, we as- sign of the DW, such as partitioning, existence of indices, or mate- sume that the concurrency control protocol provides snapshot iso- rialized views. However, as we show in §5, C JOIN can take advan- lation guarantees. In this setting, each transaction is “tagged” with tage of existing physical structures (e.g., fact table partitioning). a snapshot identifier, which is inherited by each query and update statement in the transaction. 2.2 Related Work We distinguish the class of SQL star queries that are common Our work builds builds upon a rich body of prior research and in- in DW workloads, particularly in ad-hoc data analytics. As will dustrial efforts in addressing the concurrency problem. We review be seen later, this specific query structure enables us to develop here primarily techniques that enable work sharing, which is key in efficient techniques for answering concurrent queries. Formally, a achieving high processing throughput. star query conforms to the following template: Multi-Query Optimization. When a batch of queries is optimized SELECT A, Aggr 1 , . . . , Aggr k as a unit, it becomes possible to identify common sub-expressions FROM F , Dd1 ,. . . ,Ddn V V and generate physical plans that share the common computation [21]. WHERE F 1 Ddj AND σcj (Ddj ) AND σc0 (F ) This approach requires queries to be submitted in batches, which 1≤j≤n 1≤j≤n is incompatible with ad-hoc decision support queries. Moreover, GROUP BY B common computation can be factored only within the batch of opti- Symbols A and B denote attribute sets from the referenced ta- mized queries, thus making it impossible to share work with queries bles, and Aggr 1 , . . . , Aggr k are standard SQL aggregate functions, that are already executing. In contrast, our approach shares work e.g., MIN, MAX, AVG. The WHERE clause is a conjunction of among the currently executing queries regardless of when they were 2
- 3. submitted and without requiring batch submission. query using the same plan—a single pass over a fully de-normalized, Work Sharing. Staged database systems [11, 12] enable work in-memory fact table—thus incurring more or less the same ex- sharing at run-time through an operator-centric approach. Essen- ecution cost. C JOIN achieves a similar goal, in that it enables tially, each physical operator acts as a mini query engine that ser- predictable execution times for star queries. The key differences vices several concurrent queries, which in turn enables dynamic compared to BLINK are that we do not require the database to be memory-resident, we do not require the fact table to be de- work sharing across several queries. A hash join operator, for in- normalized, and our design directly supports high query concur- stance, can share the build phase of a relation that participates in different hash joins in several queries. This design was shown to rency, whereas BLINK targets the execution of one query at a time. scale well to tens of complex queries. Our approach adopts a sim- ilar work-sharing philosophy, but customizes it for the common 3. THE CJOIN PIPELINE class of star queries. As a result, our design can scale to a sub- This section details the design of C JOIN. We first provide an stantially larger number of concurrent queries. overview of C JOIN, using an illustrative example (§3.1) and then In the Redbrick DW [9], a shared scan operator was used to share describe the various components in more detail (§3.2-§3.4). For disk I/O among multiple scan operations executing concurrently on clarity, we initially assume a query-only workload that references multiple processors; however, the in-memory data and the state of the same snapshot of the data. We then expand our discussion to other operators were not shared. Cooperative scans [24] improve mixed workloads of both queries and updates in §3.5. data sharing across concurrent scans by dynamically scheduling queries and their data requests, taking into account current sys- Notation. In what follows, we write Q to denote the set of con- tem conditions. Qiao et al. [18] have investigated shared memory current star queries that are being evaluated. We assume that each scans as a specific form of work sharing in multi-core systems: by query is assigned a unique positive integer identifier, and we use scheduling concurrent queries carefully, tuple accesses can be co- Qi to denote the query with id i. These identifiers are specific to ordinated in the processor’s cache. Our approach also leverages a C JOIN and can be assigned when queries are registered with the form of scan sharing, but targets large warehouses, where the fact operator. Also, an identifier can be reused after a query finishes its relation cannot fit in main memory. In addition to I/O, our approach evaluation. The maximum query id in Q is denoted as maxId (Q). also shares substantial computation across concurrent queries. We note that maxId (Q) ≥ |Q| in the general case, since we do not Recent work [8, 18] has investigated work-sharing techniques for require query identifiers to be consecutive. Moreover, we expect the computation of aggregates on chip multiprocessors. The devel- that maxId (Q) is bounded by a system parameter maxConc that oped techniques essentially synchronize the execution of different limits the total number of concurrent queries. aggregation operators in order to reduce contention on the hash ta- We use cij to denote the selection predicate placed by Qi on a di- bles used for aggregate computation. As discussed later, C JOIN can mension table Dj that it references. We assume that cij ≡ TRUE be combined with these techniques in an orthogonal fashion. if no explicit predicate is placed. We also define ci0 similarly with Finally, work sharing has been investigated extensively in the respect to the fact table F . Finally, we use b to denote a bit-vector context of streaming database systems [3, 6, 7, 14, 15, 16]. By shar- of bounded length, and b[l] to denote the l-th bit. The symbol 0 ing work (or state) among continuous-query operators, a streaming denotes the bit vector with all bits set to 0. DBMS can maintain a low per-tuple processing cost and thus han- 3.1 Design Overview dle a large number of continuous queries over fast streams. These techniques are specific to streaming database systems and cannot C JOIN leverages the observation that star queries have a common be applied directly to the environment that we target. An interest- structure: they “filter” the fact table through dimension predicates. ing aspect of our proposed architecture is that it incorporates ele- Correspondingly, the architecture of C JOIN consists of a pipeline ments from continuous query processing, which in turn allow us of components, as shown in Figure 1. to transfer techniques from streaming databases to a DW setting. Aggr. For instance, C JOIN adopts the Grouped Filter operator of Mad- Continuous Scan Operator den et al. [15], but extends it to support fact-to-dimension joins and Aggr. Fact Operator arbitrary selection predicates; the original operator only supported Table Preprocessor Filter ... Filter Distributor ... range predicates on ordered attributes. Aggr. Operator In summary, C JOIN enables a deeper form of work sharing than Pipeline Manager any prior work we know of: C JOIN employs a single plan that shares I/O, join computation, and tuple storage across all C JOIN queries that are in-flight at any given point in time. Figure 1: General architecture of the CJOIN pipeline. Materialized Views. Materialized views enable explicit work shar- ing by caching the results of sub-expressions that appear in concur- The C JOIN pipeline receives its input from a continuous scan of rently executing queries. The selection of materialized views is the fact table and pipes its output to aggregation operators (either typically performed off-line, by examining a representative work- sort-based or hash-based) that compute the query results. In be- load and identifying common sub-expressions [10, 20]. Capturing tween, the fact tuples are processed through a sequence of Filters, a representative workload is a challenging task in the context of ad- one for each dimension table, where each Filter encodes the cor- hoc decision-support queries, due to the volatility of the data and responding dimension predicates of all queries in Q. In this way, the diversity of queries. Moreover, materialized views add to the C JOIN can share I/O and computation among all queries in Q. maintenance cost of the warehouse, and hence they do not offer The continuous scan implies that the operator is “always on,” i.e., clear advantages for the problem considered in this paper. a new query Q can be registered with the operator at any point in time. The Preprocessor marks the point in the scan where Q enters Constant Time Query Processing. BLINK [19] is a query pro- the operator and then signals the completion of Q when the scan cessing architecture that achieves constant response time for the wraps around at that same point. This design turns the fact table type of queries considered in our work. The idea is to run each into a “stream” that is filtered continuously by a dynamic set of 3
- 4. dimension predicates. only if the tuple is still relevant to at least one query), otherwise the We illustrate the operation of the pipeline and the basic ideas be- tuple is discarded. In this example, the first Filter outputs a tuple τ hind the design of C JOIN using the simple workload shown below: only if it joins with one of δ1 , δ2 , or δ3 . The second Filter forwards ′ ′ two star queries that join fact table F with dimension tables D1 and a fact tuple only if it joins with one of δ1 or δ2 . Since the two Fil- D2 . The queries compute different aggregates and apply different ters work in sequence, τ appears in the output of the second Filter selection predicates on D1 and D2 . only if its dimension values satisfy the predicates of Q1 or Q2 . The Pipeline Manager regulates the operation of the pipeline. SELECT Aggr 1 This component is responsible for registering new queries with Q1 FROM F τ , D1 δ, D2 δ ′ C JOIN and for cleaning up after registered queries finish executing. WHERE τ 1 δ 1 δ ′ AND σc11 (δ) AND σc12 (δ ′ ) Another important function is to monitor the performance of the pipeline and to optimize it on-the-fly to maximize query through- SELECT Aggr 2 put. For this reason and others that we mention below, it is desir- Q2 FROM F τ , D1 δ, D2 δ ′ able for the Pipeline Manager to operate in parallel with the main WHERE τ 1 δ 1 δ ′ AND σc21 (δ) AND σc22 (δ ′ ) pipeline. Therefore, this component has ideally its own execution context (e.g., a separate thread or process). Figure 2 shows a possible C JOIN pipeline for this workload. The Overall, the basic idea behind C JOIN is that fact tuples flow from following paragraphs describe the functionality of each component the continuous scan to the aggregation operators, being filtered in for this specific example. between based on the predicates of the dimension tables. At a high level, this is similar to a conventional plan that would employ a dim tuple bitvec pipeline of hash join operators to join the fact table with the di- Dimension mension tables. However, C JOIN shares the fact table scan among 1 10 Continuous fact tuple bitvec Hash Table Scan 2 11 all queries, filters a fact tuple against all queries with a single di- 11 01 3 mension table probe, and stores the union of dimension tuples se- Aggr1 Fact lected by queries. Therefore, the fundamental difference from con- Preprocessor Filter Filter Distributor ventional plans is that C JOIN evaluates all queries concurrently in Table Aggr2 a single plan that shares I/O, computation, and data. The pro- posed design also differs from previous operator-centric designs Pipeline dim tuple bitvec ' Dimension (e.g., QPipe [11]) in that it takes advantage of the semantics of star Manager 01 Hash Table 1 queries to provide a much tighter degree of integration and sharing. ' 11 2 For instance, QPipe would simulate two hash join operators with different state for each query, whereas in our design there is only one operator for all concurrent queries. Figure 2: One possible instantiation of the CJOIN pipeline for In this example we illustrated only one possible C JOIN pipeline the example queries shown above. for the sample workload. As we discuss later, there are other pos- sibilities with potentially vast differences in performance. For in- The Preprocessor receives tuples from the continuous scan and stance, it is possible to change the order in which the Filters are forwards them to the remainder of the pipeline. Each fact tuple τ is applied. Another possibility is to have the Filter operators run in augmented with a bit-vector bτ that contains one bit for each query parallel using a variable degree of parallelism, e.g., the first Filter in the workload. In this example, the bit-vector consists of two bits can employ two parallel threads while the second Filter can have such that bτ [1] = bτ [2] = 1. This signifies that, initially, every just one thread. We discuss these issues in §3.4 and §4. fact tuple is relevant for both queries Q1 and Q2 . The Distributor receives fact tuples that are relevant for at least one query in the current workload. Given a received fact tuple τ , 3.2 Query Processing the Distributor examines its bit-vector bτ and routes it to the ag- We now discuss in more detail how the C JOIN operator evaluates gregation operators of query Qi if and only if bτ [i] = 1. concurrent queries. For this part of our discussion, we assume that A Dimension hash table stores a union of the tuples of a specific the workload Q remains fixed and that the operator uses a fixed dimension table that satisfy the predicates of the current queries. In ordering of filters. We discuss later the admission of new queries our example, say the predicates of Q1 select exactly two tuples δ1 (§3.3) and the optimization of the pipeline’s filter order (§3.4). ′ and δ2 from table D1 and one tuple δ2 from D2 , while Q2 selects ′ ′ tuples δ2 and δ3 from D1 and tuples δ1 and δ2 from D2 . Each stored dimension tuple δ is augmented with a bit-vector bδ , whose 3.2.1 Dimension Hash Tables length is equal to the bit-vector bτ attached to fact tuples, with the Each dimension table Dj referenced by at least one query is following interpretation: bδ [i] = 1 iff the dimension tuple satisfies mapped to a hash table HD j , which stores those tuples of Dj that the predicates of query Qi . For instance, the bit-vector for tuple are selected by at least one query in the workload. More formally, δ1 is set as bδ1 [1] = 1 and bδ1 [2] = 0. Figure 2 illustrates the a tuple δ ∈ Dj is stored in HD j if and only if there exists a query bit-vectors for all the tuples in our example. Qi that references Dj and δ satisfies cij . Tuple δ is also associ- Each Filter retrieves fact tuples from its input queue and probes ated with a bit-vector bδ of length maxId (Q) that determines the the corresponding dimension hash table to identify the joining di- queries that select δ. This bit-vector is defined as follows: mension tuples. Given a fact tuple τ , the semantics of the foreign key join ensure that there is exactly one dimension tuple δ that cor- 8 if there is no query Qi in Q >0 responds to the foreign key value. If δ is present in the dimension > > hash table, then its bit-vector bδ is combined (using bitwise AND) <1 if Qi references Dj ∧ δ satisfies cij bδ [i] = with the bit-vector bτ of τ . Otherwise, bτ is set to 0. The Filter >0 > if Qi references Dj ∧ δ does not satisfy cij > forwards τ to its output only if bτ = 0 after the combining (i.e., 1 if Qi does not reference Dj : 4
- 5. The last case inserts an implicit TRUE predicate for a query Qi C JOIN Filtering Invariant Let Dd1 ,..., Ddm be the dimension ta- that does not reference the dimension table. The reason is that Qi bles corresponding to the first m Filters in the C JOIN pipeline, does not filter fact tuples based on Dj , so implicitly it selects all m ≥ 1. If a tuple τ appears in the output of the Filter corre- the fact tuples in Dj . The hash table also records a single comple- sponding to Ddm , then we have bτ [i] = 1 if and only if Qi ∈ Q mentary bitmap bDj defined as follows: bDj [i] = 1 if Qi does and τ satisfies the predicates of Qi on the fact table and τ joins not reference Dj and bDj [i] = 0 otherwise. Essentially, bDj is with those dimension tuples in {Dd1 , . . . , Ddm } that also satisfy the bitmap assigned to any tuple δ that does not satisfy any of the the predicates of Qi . predicates in Q and hence is not stored in HD j . Tuple τ eventually reaches the Distributor if its bit-vector is non- By definition, HD j stores only a subset of Dj . Each stored tuple zero after passing through all the Filters. Given that the Filters is further augmented with a bit-vector of size maxId (Q), which cover all the dimension tables referenced in the current workload, is a moderate memory overhead. Given that the dimension tables the invariant guarantees that bτ [i] = 1 if and only if τ satisfies all tend to grow at a much slower rate than the fact table (typically, by the selection and join predicates of Qi . a logarithmic rate [17, 23]), it is reasonable to expect that the hash The Distributor routes τ to the aggregation operator of each query tables fit in main memory for modern hardware configurations. As Qi for which bτ [i] = 1. The aggregation operator can directly ex- a concrete example, TPC-DS [23] employs 2.5GB of dimension tract any needed fact table attributes from τ . If the operator needs data for a 1TB warehouse; today, even a workstation-class machine to access the attributes on some dimension Dj , then it can use the can be economically equipped with 16GB of main memory. foreign key in τ to probe for the joining dimension tuple. A more efficient alternative is to attach to τ memory pointers to the joining 3.2.2 Processing Fact Tuples dimension tuples as it is processed by the Filters. Specifically, let We consider next the details of processing a fact tuple τ through δ be a tuple of Dj that joins to τ and assume that Qi references the C JOIN pipeline, starting with the Preprocessor. The Preproces- Dj . Based on our definition of HD j , it is possible to show that δ is sor attaches to τ a bit-vector bτ of length maxId (Q) that traces the in HD j when τ is processed through the corresponding Filter and relevance of the tuple to different queries. This bit-vector is modi- remains in memory until τ reaches the Distributor. This makes it fied as τ is processed by Filters and it is used in the Distributor to possible to attach to τ a pointer to δ after HD j is probed, so that the route τ to aggregation operators. aggregation operator can directly access all the needed information. The bit-vector is initialized based on the predicates placed on the fact table, as follows: bτ [i] = 1 if Qi ∈ Qi ∧ τ satisfies ci0 (i.e., 3.2.3 Cost of C JOIN Query Processing the selection predicate on the fact table) and bτ [i] = 0 otherwise. The design of C JOIN has specific implications on the cost of After bτ is initialized, the Preprocessor forwards it to its output query processing, which we discuss below. queue if bτ = 0. In the opposite case, τ can be safely dropped We consider first the end-to-end processing for a single fact tuple from further processing, as it is guaranteed to not belong to the through the C JOIN operator. Once a tuple is initialized in the Pre- output of any query in Q. Computing bτ involves evaluating a set processor, if K is the total number of Filters in the pipeline, then of predicates on τ , and thus it is necessary to employ an efficient processing the fact tuple involves K probes and K bit-vector AND evaluation mechanism to ensure that the Preprocessor does not be- operations in the worst case. Since the probe and the AND opera- come the bottleneck. This issue, however, is less crucial in practice, tion have limited complexity, and assuming that the Preprocessor since most queries place predicates solely on dimension tables. can initialize efficiently the bit-vector of the tuple, C JOIN can sus- Tuple τ passes next through the sequence of Filters. Consider tain a high throughput between the continuous scan and the aggre- one such filter, corresponding to dimension table Dj . Let δ be the gation operators. Moreover, the reliance on sequential scans as the joining dimension tuple for τ . The Filter probes HD j using the sole access method allows C JOIN to scale gracefully to large data foreign key of τ and eventually computes (as explained in the next sets, without incurring the costs of creating and maintaining mate- paragraph) a “filtering bit-vector” denoted by bτ 1HD j , which re- rialized views or indices on the fact table, or maintaining statistics. flects the subset of queries that select δ through their dimension We discuss now the cost of a single query. The response time of predicates. The Filter thus joins τ with Dj with respect to all a query evaluated with C JOIN is dominated by the time required to queries in the workload by performing a single probe to HD j . Sub- loop around the continuous scan. This cost is relatively stable with sequently, bτ is bitwise ANDed with bτ 1HD j . If this updated bτ respect to the total number of queries in the workload, because the vector is 0, then the fact tuple can safely be dropped from further I/O is shared across all queries and the cost of probing in each Fil- processing, since it will not belong to the output of any query in Q; ter (cost of a hash table lookup and cost of a bitwise AND) grows otherwise it is passed to the output of the Filter. As an optimization, at a low rate with the number of queries. Thus, as long as the rate it is possible to avoid completely the probing of HD j by checking of query submission does not surpass the rate of query completion, first whether bτ AND ¬bDj is 0 (i.e., Dj does not appear in any C JOIN yields response times with low variance across different de- query Qi to which τ is relevant). In this case, τ is not relevant to grees of concurrency. This property is crucial if we are to scale any queries that reference HD j and can be simply forwarded to the effectively to a large number of concurrent queries. next Filter. An added bonus is that the current point in the continuous scan The filtering bit-vector is computed as follows: if the probe finds can serve as a reliable progress indicator for the registered queries, δ in HD j then bτ 1HD j = bδ , similar to the example of Figure 2; and it is also possible to derive an estimated time of completion otherwise, bτ 1HD j is set to bDj , the bit-vector of any tuple that based on the current processing rate of the pipeline. Both of these is not stored in HD j . Given the definitions of bδ and bDj , we metrics can provide valuable feedback to users during the execution can assert the following key property for the filtering bit-vector: of ad-hoc analytic queries in large data warehouses. bτ 1HD j [i] = 1 if and only if either Qi references Dj and δ is The predictability property implies that query response time is selected by Qi , or Qi does not reference table Dj . This property bounded below by the cost of a full sequential scan of the fact ta- ensures that bτ AND bτ 1HD j results in a bit-vector that reflects ble. Conventional physical plans for star queries are likely to have accurately the relevance of τ to workload queries up to this point. the same property; for instance, a common plan in commercial sys- This can be stated formally with the following invariant: tems is a left-deep pipeline of hash joins with the fact table as the 5
- 6. outer relation. In principle, the large table scan can be avoided Algorithm 1: Admitting a new query to the C JOIN pipeline. by the use of indices or materialized views, but these structures Input: Query Qn are generally considered too expensive in the DW setting, because Data: A list L of dimension hash tables, initially empty fact table indices have a prohibitively high maintenance cost, and 1 Let D be the set of dimension tables referenced by Qn ad-hoc data analysis workloads may not be stable enough to iden- 2 Let D ′ be the set of dimension tables in the pipeline tify useful views to materialize. A common method in practice is 3 foreach Dj ∈ D ∪ D ′ do to limit queries on specific partitions of the fact table; as will be 4 if Dj is not in the pipeline then 5 Initialize HD j and bDj based on Q ∪ {Qn } discussed in §6, this method can also be integrated in C JOIN with 6 Append HD j to L similar benefits. In any case, we stress that C JOIN becomes yet one 7 else if Dj is referenced by Qn then more choice for the database query optimizer; it is always possi- 8 bDj [n] = 0 ble to execute queries with conventional execution plans if this is 9 else estimated to be more efficient. 10 bDj [n] = 1 3.3 Query Admission and Finalization 11 foreach Dj ∈ D do 12 foreach δ ∈ σcnj (Dj ) do Up to this point, we have examined the processing of fact tu- 13 if δ is not in HD j then ples assuming that the C JOIN pipeline has been initialized correctly 14 Insert δ in HD j with respect to a given workload. In this section, we discuss how 15 bδ ← bDj the state of the C JOIN pipeline is updated when a new query is ad- 16 bδ [n] ← 1; mitted, or when an existing query finishes its processing. We use n to denote the id of the query in question. For a new 17 Stall Preprocessor; query, n is assigned as the first unused query id in the interval 18 foreach HD j in L do insert a Filter for HD j 19 Q ← Q ∪ {Qn }; [1, maxConc], where maxConc is the system-wide limit on the 20 Set start of Qn to next tuple in Preprocessor’s input maximum number of concurrent queries. To simplify our presenta- 21 Append a control tuple τQn in Preprocessor’s output tion, we assume without loss of generality that n ≤ maxId (Q). 22 Resume Preprocessor 3.3.1 Admitting New Queries The registration of Qn is done through the Pipeline Manager, which orchestrates the update of information in the remaining com- will not miss any relevant fact tuples. ponents. This approach takes advantage of the fact that the Pipeline It is important to note that query registration occurs in the Pipeline Manager executes in parallel with the C JOIN pipeline, thus mini- Manager thread and thus it can proceed, up to line 17, in parallel mizing the disruption in the processing of fact tuples. with the processing of fact tuples through the pipeline. This ensures The registration is performed in the Pipeline Manager thread us- that other queries are minimally disrupted during the registration of ing Algorithm 1. The first step is to update bit n of bDj for each Qn . The concurrent update of the bit-vectors in dimension hash ta- dimension table that is referenced by Qi or appears in the pipeline bles does not compromise the correctness of results, since the Pre- (line 3). Subsequently, the algorithm updates the hash tables for processor continues to mark each fact tuple as irrelevant to query the dimensions referenced in the query (line 11). For each such di- Qn (bτ [n] = 0). Thus, even if bδ [n] is switched on for some tuple mension table Dj , the Pipeline Manager issues the query σcnj (Dj ) δ (line 16), it does not lead to the generation of results for Qn until and updates HD j with the retrieved dimension tuples. If a retrieved after it becomes part of the workload in line 19, because bit n in tuple δ is not already in HD j , then δ is inserted in HD j and its bit- the fact tuples’ bit-vectors will be 0 until that point. vector initialized to bDj . We then set bδ [n] ← 1 to indicate that δ is of interest to Qn . At the end of these updates, all the dimension 3.3.2 Finalizing Queries hash tables are up to date with respect to the workload Q ∪ {Qn }. Query Qn is finalized when the continuous scan wraps around Having updated the dimension tables, the algorithm completes the starting fact tuple τ . Upon encountering τ in its input, the Pre- the registration by installing Qn in the Preprocessor and the Dis- processor first removes Qn from Q, which ensures that the bit- tributor. This involves several steps. First, the Pipeline Manager vector of τ (and of any subsequent tuple) will have bit n switched suspends the processing of input tuples in the Preprocessor, which off. This ensures that Qn becomes irrelevant for the filtering of stalls the pipeline (line 17). This enables the addition of new Fil- fact tuples. Subsequently, the Preprocessor emits an “end of query” ters in the pipeline to cover the dimension tables referenced by the control tuple that precedes τ in the output stream. The control tu- query. (While new Filters are appended in the current pipeline, ple is handled in a fashion similar to the query-start tuple and is their placement may change as part of the run-time optimization— forwarded through the pipeline to the Distributor, which finalizes see §3.4.) Q is also updated to include Qn , which allows bit n of the aggregation operators of Qn and outputs their results. Since the the fact tuple bit-vector to be initialized correctly. Next, the first control tuple precedes τ , we ensure that the aggregation operators unprocessed input fact tuple, say τ , is marked as the first tuple of of Qn will not consume any fact tuple more than once. Qn , so that it is possible to identify the end of processing Qn (see The final step is to clear the dimension hash tables from any in- next paragraph). Finally, a special “query start” control tuple τn formation pertinent to Qn . This is handled in the Pipeline Man- that contains Qn is appended to the output queue of the Preproces- ager thread according to Algorithm 2, which essentially reverses sor, and the Preprocessor is resumed. The control tuple precedes the updates performed when the query was admitted. This clean- the starting tuple τ in the output stream of the Preprocessor and is up may render certain information in the hash tables useless. For forwarded without filtering through the Filters and on to the Dis- instance, if for some tuple δ in HD j we have δ[i] = 0, then δ can tributor. In turn, the latter uses the information in τQn to set up the be removed. In turn, if HD j becomes empty, then it can be re- aggregation operators for Qn . Since τQn precedes any potential moved from the pipeline along with the corresponding Filter. Of results for Qn (the pipeline preserves the order of control tuples course, the latter requires a stall of the pipeline in order to recon- relative to data tuples), we guarantee that the aggregation operators figure the Filter sequence. Note that this “garbage collection” can 6
- 7. Algorithm 2: Removing a finished query from the pipeline. imizes the expected processing cost of each stream tuple. The cor- Input: Query Qn . respondence to C JOIN appears when viewing Filters as predicates, Data: A list L of dimension hash tables, initially empty. and the continuous scan as an infinite stream. Moreover, since each 1 Let D be the set of dimension tables referenced by Qn ; Filter has a fixed cost—one probe of the in-memory hash table 2 Let D ′ be the set of dimension tables in the pipeline ; and one bitwise AND operation—minimizing the expected process- 3 foreach Dj ∈ D ′ do ing cost is equivalent to minimizing the expected number of Filter 4 bDj [n] = 1; probes. In our work, we employ the techniques of Babu et al. [5] 5 foreach Dj ∈ D do to implement the run-time optimization of the Filter ordering. A 6 foreach δ ∈ HD j do detailed discussion of these techniques is beyond the scope of our 7 bδ [n] ← 0; paper. We do note, however, that other techniques are applicable 8 if bδ = 0 then remove δ from HD j too, such as those introduced by Liu et al. [13]. 9 if HD j = ∅ then Append HD j to L 10 if L = ∅ then 3.5 Handling Updates 11 Stall pipeline; Up to this point, we have considered the case of read-only trans- 12 foreach HD j ∈ L do remove corresponding Filter; actions that reference the same data snapshot. This enables group- 13 Resume pipeline; ing all queries of these transactions in the same C JOIN operator that performs a single continuous scan of the specific snapshot. In the remainder of this section we examine adaptations of C JOIN be done asynchronously (as long as the query identifiers are cor- when this assumption is relaxed, i.e., when the queries correspond rectly handled); one could also maintain usage bits and evict the to transactions with different snapshot ids. (As mentioned in §2, least-recently-used tuples according to memory needs. we assume snapshot-based isolation, since this is the norm in prac- tice.) This scenario arises when read-only transactions are inter- 3.3.3 Correctness leaved with updates, or when the same transaction contains both The correctness of C JOIN with respect to query finalization hinges queries and updates. In all cases that we examine, we focus on up- upon two properties. First, the continuous scan returns fact tuples in dates that reference only the fact table. In the rare event of updates the same order once resumed. This is necessary so that the Prepro- on dimension tables, we assume that the admission of new queries cessor can identify correctly when the fact table has been scanned in C JOIN is serialized with the transaction of the update. exactly once for each query. It is reasonable to expect that this prop- We consider two possibilities for adapting C JOIN to this sce- erty holds for real-world systems. The second property is that, if a nario, that depend on the functionality of the continuous scan op- control tuple τ ′ is placed in the output queue of the Preprocessor erator. The first possibility is that the continuous scan operator can before (respectively after) a fact tuple τ , then τ ′ is not processed in return all fact tuples corresponding to the snapshots in the current the Distributor after (respectively before) τ . This property guaran- query mix. This essentially requires the scan to expose the multi- tees that the aggregation operators of a query neither miss relevant version concurrency control information for the retrieved fact tu- tuples nor process them more than once. This property needs to be ples. Then, the association of a query Qi to a specific snapshot can enforced by the implementation of the C JOIN pipeline. be viewed as a virtual fact table predicate, and it can be evaluated by the Preprocessor over the concurrency control information of each 3.4 Pipeline Optimization fact tuple. The remaining C JOIN mechanism remains unchanged. Of course, the benefits of the C JOIN operator are decreased as the The order of Filters in the pipeline influences performance, be- snapshots referenced by the transactions become disjoint, but we cause it determines the expected number of probes for each fact believe this case to be infrequent in practice. tuple. Drawing a correspondence to the ordering of joins in a sin- The second possibility is when the previous functionality is not gle query plan, we expect that a good order will apply the most provided, i.e., the scan only returns tuples of a specific snapshot. In selective Filters first, in order to drop fact tuples early. We there- this case, we create several C JOIN operators, one for each snapshot fore face the following optimization problem: Given a workload Q that is referenced, and register queries to the respective operator. and a C JOIN pipeline for Q, determine an ordering of the Filters This approach could degenerate into a single plan per query, if each that minimizes the expected number of probes for each fact tuple. transaction in our workload mix referenced different snapshot ids. One complicating factor is that the selectivity of each Filter de- This, however, is an exceptionally rare event in practice. pends on the workload Q, since a Filter encodes the join predicates of several queries on a specific dimension table. Thus, if the work- load is unpredictable, as is the case with ad-hoc analytics in a data 4. CJOIN IMPLEMENTATION warehouse, then the optimal order might change as the query mix In this section, we discuss the implementation of C JOIN on a changes. This observation suggests an online approach to optimiz- multi-core system, the predominant hardware architecture in real- ing the order of Filters in the C JOIN pipeline. The idea is to monitor world deployments today and in the near future. Nevertheless, we at run-time the selectivity of each Filter and then optimize the order expect C JOIN to yield significant benefits on single-core/single- based on the gathered statistics. This continuous process of mon- CPU hardware as well. itoring and re-optimizing can be performed asynchronously inside An efficient implementation of C JOIN on a multi-core architec- the Pipeline Manager thread. ture requires that the operator’s components (Preprocessor, Filters, Previous work introduced several techniques for optimizing the and Distributor) be mapped to multiple threads, which in turn are execution order of relational operators on-the-fly [4, 5, 13]. In par- mapped by an operating system to different processor cores. As an ticular, the optimization of the C JOIN pipeline maps precisely to example, one obvious mapping is to assign each component to a the following problem that has been investigated in the context of different thread and then employ tuple queues to link the pipeline. streaming database systems: We are given a conjunction of pred- However, the mapping of C JOIN components to threads must strike icates that are applied on the tuples of an infinite stream, and the a balance between the degree of parallelism, the overhead of pass- goal is to determine an order for evaluating the predicates that min- ing tuples between the threads, and the utilization of processor 7
- 8. caches. Passing a tuple from one thread to another requires syn- thread retrieve or deposit tuples in batches, whenever possible. Fi- chronization between the threads and also results in data cache nally, we reduce the cost of memory management synchronization misses if the two threads execute on different cores. On the other by using a specialized allocator for fact tuples. The specialized al- hand, executing components in different threads improves cache locator preallocates data structures for all in-flight tuples, whose locality if the internal state is read-mostly (such as the dimension number is determined based on the upper bound on the length of a hash tables) and can be partitioned among multiple threads. tuple queue and the upper bound on the number of threads. Given Since the internal states of the Preprocessor and Distributor are the pool of preallocated tuples, the allocator reserves and releases frequently updated, we chose to map each to a single thread as tuples using bitmap operations, which entail a single machine in- shown in Figure 3. Filters, where the bulk of C JOIN processing struction on most CPUs, thus being both atomic and efficient. happens, do not have any internal state other than the dimension hash tables, which are read-mostly. Our implementation allows for a flexible mapping of Filters to threads by collapsing multiple ad- 5. EXTENSIONS jacent Filters to a Stage (to reduce the overhead of passing tuples In this section, we revisit some of the assumptions made in §2. between the threads) and assigning multiple threads to each Stage We discuss ways in which C JOIN can be adapted to accommodate (to increase parallelism). This approach gives rise to the following the lifting of these assumptions. possible configurations: Galaxy Schemata. A galaxy schema involves several fact rela- • A vertical configuration assigns a single Stage to each Filter, with tions, each of which is the center of a star schema. Star queries a (potentially) different number of threads per Stage. This design remain common in this setting and can thus be evaluated using favors the affinity of Stages to cores so that instruction and data C JOIN, but it is also common to observe queries involving the join locality is maximized. On the other hand, we expect a large number of several fact tables (typically two). of data cache misses when tuples are transferred between Filters. C JOIN can benefit the evaluation of these queries even though Moreover, the problem of pipeline optimization now acquires an it was not designed for this specific case. Concretely, consider a extra free variable: the number of threads per Stage. query Q with a single fact-to-fact join predicate. By using the fact- to-fact join as a pivot, we can express the evaluation of Q as the • A horizontal configuration assigns a single Stage to the entire join between the results of two star queries, say Qa and Qb , over sequence of Filters, and all the threads are assigned to this single the corresponding fact tables. It now becomes possible to register Stage. This implies that several copies of the Filter sequence are each Qi with the C JOIN operator that handles the concurrent star running in parallel (one for each thread) and accessing the same queries on the corresponding fact table, the difference being that hash tables. This scheme avoids data cache misses when tuples are the Distributor pipes the results of Qi to a fact-to-fact join operator passed between Filters, but may incur more misses on the accesses instead of an aggregation operator. Notice that each C JOIN operator of the hash tables, since each thread needs to access more data. will be evaluating concurrently several star queries that participate Pipeline optimization involves solely ordering the Filters. in concurrent fact-to-fact join queries. Thus, the overall idea is to • A hybrid configuration employs several Stages and an assign- use C JOIN as a physical operator that can evaluate efficiently the ment of threads per Stage. This configuration can strike a balance “star sub-plans” of bigger query plans. between the two extremes of a horizontal vs. vertical configuration. Column Stores. Column stores have been gaining traction as a More concretely, the cost of tuple passing is incurred only between scalable system architecture for large data warehouses [1, 2, 22]. It Stages, and each thread needs to access solely the dimension ta- is possible to adapt C JOIN in this setting as follows: The continuous bles that exist within a Stage. However, the run-time optimization fact table scan can be realized with a continuous scan/merge of only becomes more complex, as there are now three free variables: the those fact table columns that are accessed by the current query mix. order of Filters, the boxing of Filters in Stages, and the assignment Thus, C JOIN can take advantage of the columnar store in order of threads to Stages. to reduce the volume of data transferred by the scan. The other Stage Stage case that we need to examine is the evaluation of filter queries over dimension tables, which occurs as part of a new query registration. This case is readily handled by the column store, since C JOIN uses the existing query processing infrastructure to retrieve the resulting dimension tuples. Preprocessor Filter Filter Filter Filter Filter Distributor Compressed Tables. Data warehouses may employ compression to reduce the amount of I/O and memory bandwidth used for data transfer [1, 19]. C JOIN makes no assumptions about the physi- Figure 3: An example mapping of a CJOIN pipeline to threads. cal storage of tuples, except that it is possible to evaluate predi- cates, extract fields, and retrieve result tuples for dimension queries. Thus, compression of tables is an orthogonal technique that can be Our experiments indicate that the extra parallelism resulting from using multiple Stages does not outweigh the cost of forwarding the easily incorporated in C JOIN. For instance, the continuous scan tuples between them. Consequently, we henceforth assume the hor- can bring in compressed tuples and decompress on-demand and on- izontal configuration, and we achieve parallelism by allocating sev- the-fly as needed for probing the dimension hash tables. Another option is to use the partial decompression technique proposed in eral threads to the single Stage. BLINK [19] in order to evaluate predicates efficiently on the com- A few well-known design principles turned out to be crucial to achieving good C JOIN performance in our prototype. To reduce pressed fact table. the overhead of thread scheduling, we wake up a consumer thread Fact Table Partitioning. The organization of the fact table in parti- only when its input queue is almost full. Similarly, we resume the tions may arise naturally from the operational semantics of the DW, producer thread only when its output queue is almost empty. We e.g., the fact table may be range-partitioned by a date attribute cor- also reduce the overhead of queue synchronization by having each responding to the loading of new data. The optimizer can take ad- 8
- 9. vantage of this partitioning in order to limit the execution of a query 6.1.1 Systems to a subset of the fact table. Thus, a query that sets a range pred- Our C JOIN prototype is implemented as a multi-threaded pro- icate on the partitioning date attribute will need to examine only a cess executing on top of the PostgreSQL database system. C JOIN subset of the partitions. In principle, this approach can reduce sig- uses PostgreSQL to issue queries over the dimension tables for the nificantly the response time of an individual query, but concurrent registration of new queries. The continuous scan is implemented queries can still lead to random I/O, which has crippling effects on by issuing successive SELECT * FROM F queries to PostgreSQL. overall performance. To increase the throughput of the scan, we have implemented a C JOIN can take advantage of partitioning in order to reduce the fast tuple copy mechanism between PostgreSQL and C JOIN using volume of data accessed by the continuous scan and also to reduce a shared memory buffer. Our prototype supports both the horizontal query response time. More concretely, the query registration algo- (one Stage for all Filters) and vertical (one Stage per Filter) config- rithm can be modified to tag each new query with the set of parti- urations described in §4. tions that it needs to scan. This set can be determined by correlating We compare C JOIN to both a widely used commercial database the selection predicates on the fact table with the specific partition- system (henceforth referred to as “System X”) and PostgreSQL. We ing scheme. The Preprocessor can then realize the continuous scan tune both systems (e.g., computation of optimization statistics, al- as a sequential scan of the union of identified partitions. At the end lowing a high number of concurrent connections, scans using large of each partition, the end-of-query control tuple can be emitted for data chunks, etc.) to ensure that the experimental workloads are the queries that have covered their respective set of partitions, thus executed without obvious performance problems. We have veri- allowing queries to terminate early. fied that both systems employ the same physical plan structure to Efficient Aggregate Computation. The current C JOIN design for- evaluate the star queries in the experimental workloads, namely, a wards the resulting tuples to aggregation operators that compute pipeline of hash joins that filter a single scan of the fact table. The the final query results. There may be opportunities to optimize this small size of the dimension tables implies that they can be cached final stage, e.g., by sharing work among aggregation operators, de- efficiently in main memory and hence their processing is expected pending on the current query mix. This optimization is orthogonal to be very fast. As a result, we do not tune the physical design of to C JOIN and can be performed using existing techniques [8, 18]. any of the database systems with indices or materialized views on the dimension tables, since this would not improve query response Memory-resident Databases. The design of C JOIN was motivated time (we verified this claim for the experimental workloads). We by large-scale data warehouses, where the fact table is orders of also avoid using indices and views on the fact table, for the obvi- magnitude larger that the available main memory. However, it is ous reasons mentioned in previous sections. For PostgreSQL, we straightforward to employ C JOIN for a memory-resident data set as enable the shared-scans feature to maximize its work sharing. well. One difference is that the sharing of the continuous scan may Our experimental server has two quad-core Intel Xeon CPUs, not have as significant an effect as when the fact table resides on with a unified 6 MB L2 cache on each CPU shared among all 4 disk. Still, C JOIN will enable work sharing among the concurrent cores and 8 GB of shared RAM. The machine has four HP 300GB queries, which is important in achieving high throughput. 15K SAS disks, arranged in a hardware-controlled RAID-5 array. Indexes and Materialized Views. As discussed earlier, fact table indexes are not likely to be useful in the DW setting that we con- 6.1.2 Data Set and Workload sider, due to their high maintenance cost. Similarly, the inherent We employ the data set and queries defined in the Star Schema volatility of ad-hoc queries limits the appearance of common pat- Benchmark (SSB) [17]. We choose this particular benchmark be- terns and hence the importance of materialized views that involve cause it models a realistic DW scenario and targets exactly the class the fact table. It is more common (and affordable) for data ware- of queries that we consider in our work. houses to maintain indexes and views on dimension tables. C JOIN We generate instances of the SSB data set using the data genera- takes advantage of these structures transparently, since they can op- tor supplied with the benchmark. The size of each instance is con- timize the dimension filter queries that are part of new query regis- trolled by a scale factor parameter denoted as sf . A value sf = X tration (see also Algorithm 1). results in a data set of size X GB, with 94% of the data correspond- ing to the fact table. We limit the maximum value of the scale factor 6. EVALUATION to 100 (i.e., a 100GB data set) to ensure the timely execution of the This section reports the results of an experimental evaluation of test workloads on our single experimental machine. our C JOIN prototype. We investigate the performance characteris- We generate workloads of star queries from the queries speci- tics of C JOIN and compare it to real-world database systems using fied in the benchmark. Specifically, we first convert each bench- workloads of different characteristics. In particular, we focus on mark query to a template, by substituting each range predicate in the following high-level questions: the query with an abstract range predicate, e.g., d_year >= 1992 and d_year <= 1997 is converted to d_year >= X and d_year • Which is the best way to map the components of a C JOIN pipeline <= Y, where X and Y are variables. To create a workload query, we to CPUs? (§6.2.1) first sample a query template and then substitute the abstract ranges • How does C JOIN throughput scale with increasing numbers of with concrete predicates based on a parameter s that controls the se- concurrent queries? (§6.2.2) lectivity of the predicate. Thus, s allows us to control the number • How sensitive is the throughput of C JOIN to workload character- of dimension tuples that are loaded by C JOIN per query, as well as istics? (§6.2.3) the size of the hash tables in the physical plans of PostgreSQL and • How does the size of a data warehouse impact C JOIN’s perfor- System X. mance? (§6.2.4) Note that the original benchmark specification contains 13 queries of varying complexity. We excluded queries Q1.1, Q1.2 and Q1.3 6.1 Methodology from the generation of workload queries because they contain se- We describe here the systems, data sets, workloads, and evalua- lection predicates on fact table attributes, and this functionality is tion metrics that characterize our experiments. not yet supported by our prototype. This modification does not af- 9
- 10. fect the usefulness of the generated workloads, since the omitted Horizontal Config Ver cal Config queries are the simplest ones in the SSB benchmark and the only 1200 Throughput (queries/hour) ones that do not have a group-by clause. 1000 6.1.3 Evaluation Metrics 800 We measure the performance of a system with respect to a spe- 600 cific workload using query throughput (in queries per hour) and the 400 average and standard deviation of response times for each of the 10 200 SSB query templates. We employ the standard deviation to quan- tify performance stability and predictability. 0 1 2 3 4 5 For each tested system, we execute the workload using a single client and a cold cache. The degree of query concurrency is con- Number of threads trolled by an integer parameter n, as follows: the client initially submits the first n queries of the workload in a batch, and then sub- Figure 4: The effect of pipeline configuration on performance. mits the next query in the workload whenever an outstanding query finishes. This way, there are always n queries executing concur- rently. To ensure that we evaluate the steady state of each system, Ideally, a system with infinite resources would exhibit linear scal- we measure the above metrics over queries 256...512 in the work- ing: an increase of n by a factor k would increase throughput by the load (n = 256 is the highest degree of concurrency in our experi- same factor. In practice, we expect a sub-linear scale-up, due to the ments). The fact that we measure a fixed set of queries allows us to limited resources and the interference among concurrent queries. make meaningful comparisons across different values of n. Figure 5 shows query throughput for the three systems as a func- tion of n (measurements are gathered with a 100GB data set and 6.2 Experiments selectivity s = 0.01). An immediate observation is that C JOIN de- This section presents a subset of the experiments that we con- livers a significant improvement in throughput compared to System ducted to evaluate the effectiveness of the C JOIN operator. X and PostgreSQL. The improvement can be observed for n ≥ 32 and reaches up to an order of magnitude for n = 256. 6.2.1 Pipeline Configuration We begin with a comparison of the vertical and horizontal C JOIN CJOIN System X PostgreSQL configurations that are supported by our prototype. The vertical 1600 Throughput (queries/hour) configuration maps each Filter to a distinct Stage, which implies 1400 that Filters work in parallel with each other. The horizontal con- 1200 figuration boxes all Filters in a single Stage that is assigned several 1000 threads. Thus, each thread evaluates in parallel the sequence of 800 Filters for a subset of the fact tuples. As discussed in §4, the ver- 600 tical and horizontal configurations represent the two extremes for 400 mapping the C JOIN operator to a multi-core system. 200 We evaluate the performance of each configuration as we vary 0 the total number of threads in C JOIN. Each configuration has the 0 32 64 96 128 160 192 224 256 minimum number of threads needed for its execution; we also set Number of concurrent queries an upper limit so that each CPU core does not execute more than one “active” thread. Specifically, we always set aside three cores for the PostgreSQL process and the Preprocessor and Distributor Figure 5: Query throughput scale-up with number of queries. threads. This leaves five cores out of the eight available on our experimental machine, so we use this number as the upper limit for C JOIN achieves the ideal linear scale-up for 1 ≤ n ≤ 128. In- the number of Stage threads. For the horizontal configuration, all creasing n from 128 to 256 results in a sub-linear query throughput available threads go to the single Stage. The vertical configuration increase of 133%. We profiled the C JOIN executable and found that requires at least four threads (there are four Filters corresponding bitmap operations took up a large fraction of running time for this to the dimension tables in the SSB data set) and, if there is a fifth particular n, and so we believe that the sub-linear scale-up is due thread available, we assign it to the first Stage. mostly to the specific bitmap implementation we employ. Since Figure 4 shows the query throughput of the two configurations the efficiency of bitmap operations is crucial for C JOIN’s scalabil- as we vary the number of Stage threads. The results show clearly ity, we plan to replace the bitmap implementation. that the horizontal pipeline configuration consistently outperforms Unlike C JOIN, the query throughputs of System X and Post- the vertical configuration, as long as it has more than one thread greSQL actually decrease when the number of concurrent queries assigned to the single Stage. Upon closer inspection, we found that increases past 32. As expected, this decrease is a consequence of an the overhead of passing tuples between threads, which includes L2 increased competition among all concurrently executing queries for data cache misses and thread synchronization, outweighs the ben- both I/O bandwidth (for scan) and main memory (for hash tables). efits gained by the parallelism of the vertical configuration. Based We examine next the predictability of each system with respect on these results, we focus the subsequent experiments on the hori- to query response time. A system with predictable performance zontal configuration for the C JOIN operator. delivers a constant query response time independently of the num- ber of queries that execute concurrently. To quantify this notion 6.2.2 Influence of Concurrency Scale of predictability, we report the response times of queries generated The next set of experiments evaluates the performance of the from the template corresponding to SSB query Q4.2, which is one three systems as we increase n, the degree of query concurrency. of the most complex queries in the benchmark (it joins with more 10
- 11. dimension tables than most other queries and the cardinality of its Figure 7 shows query throughput for all three systems as a func- Group-By is among the largest). The results are qualitatively the tion of s (we again use a 100 GB data set with n = 128 concur- same for the other templates in the benchmark. rent queries). First, we observe that C JOIN continues to outper- Figure 6 shows the average response time for queries conforming form System X and PostgreSQL for all settings of s. However, to template Q4.2 as a function of n. When increasing the number we observe that the gap is reduced when s = 10%, which we in- of concurrent queries n from 1 to 256, the response time of System vestigate below. Second, query throughputs of C JOIN and System X grows by a factor of 19 and the response time of PostgreSQL X do indeed drop approximately linearly with s as expected. We grows by a factor of 66. These are precisely the undesirable perfor- cannot draw any conclusions about PostgreSQL, because we have mance patterns that lead to “workload fear” in existing DW plat- only two data points: for s = 10%, we terminated the experiment, forms. C JOIN response time, on the other hand, grows by less than because PostgreSQL took excessive amounts of time. Overall, we 30%, which is a small degradation in performance if one takes into find C JOIN reacts predictably to changes in workload selectivity. account that the number of queries range over two orders of mag- nitude. Our measurements of deviation indicate that all systems CJOIN System X PostgreSQL deliver relatively stable query response times in steady state, al- 1200 Throughput (queries/hour) though C JOIN does better: the standard deviation of response time is within 0.5% of the average for C JOIN, 5% for System X, and 9% 1000 for PostgreSQL. 800 600 CJOIN System X PostgreSQL 400 30 200 Query response me (x 1,000 seconds) 25 0 20 0 1 2 3 4 5 6 7 8 9 10 15 Predicate selec vity (%) 10 5 Figure 7: Influence of query selectivity on throughput. 0 0 32 64 96 128 160 192 224 256 As noted above, the performance of C JOIN decreases signifi- Number of concurrent queries cantly for higher values of s. Essentially, the dimension hash ta- bles have to hold an increased number of tuples, which has adverse effects on cache locality and hence access times. Moreover, as we Figure 6: Predictability of query response time. explain below, the overhead of submitting new queries grows sub- stantially, which contributes to the slow down of the operator. At this point, we quantify the overhead of query submission in Table 2 reports the overhead of new query submission for differ- C JOIN as we vary n. We focus again on queries matching tem- ent values of s. When s increases, it is more expensive to evaluate plate Q4.2 and measure the total time from the submission of the the predicates of newly submitted queries. The dimension hash ta- query up until the point the “start query” control tuple is inserted bles also grow larger, and hence it is more expensive to update them in the pipeline. This period represents the interval during which when a new query arrives. On the other hand, there are fixed costs the submitted query competes for resources with the remainder of of new query admission that do not depend on s, including the de- the pipeline, and thus it is interesting to examine its magnitude for lay to submit predicate queries to the underlying PostgreSQL, to different parameters of the workload. disconnect and drain the pipeline, and to update the metadata that Table 1 shows that the time to submit a query does not depend on tracks active queries in the system. As shown in the table, the fac- the number of active queries. Moreover, the “interference” interval tors independent of s are significant for s ≤ 1%, but the factors is small compared to the total execution time of each query. These dependent on s become dominant for s = 10%. results indicate a negligible overhead for registering a query. Predicate selectivity (%) 0.1 1 10 n 32 64 128 256 Submission time (sec) 1.6 2.4 11.6 Submission time (sec) 2.4 2.4 2.4 2.3 Response time (sec) 707.2 759.0 3418.0 Response time (sec) 724.8 723.1 759.0 861.2 Table 2: Influence of predicate selectivity on query submission Table 1: Influence of concurrency on query submission time. time. 6.2.3 Influence of Predicate Selectivity 6.2.4 Influence of Data Scale In the next set of experiments we evaluate the performance of In the next set of experiments, we evaluate the performance of the three systems as we increase s, the selectivity of the query the three systems as we increase sf , the scale factor that controls template predicates. Increasing s forces all evaluated systems to the size of the SSB data set. A scale factor sf = α implies a data access more data to answer queries. Therefore, we expect the per- set of α GB. Ideally, query throughput is inversely proportional formance to degrade at least linearly with s. However, other factors to sf , since queries should take k times longer to complete on a may contribute to a super-linear degradation, e.g., hash tables may k-times larger data set. Consequently, we expect the normalized not fit into L2 caches, or System X and PostgreSQL may thrash by query throughput, defined as a product of query throughput and sf , spilling data to temporary disk files. to remain approximately constant as sf increases. 11
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