Gossip-based algorithms

Epidemic Algorithms
Amir H. Payberah
amir@sics.se
Amirkabir University of Technology
(Tehran Polytechnic)
Amir H. Payberah (Tehran Polytechnic) Epidemic Algorithms 1393/7/7 1 / 60

What is the Problem?

Application-level broadcast/multicast

Application-level broadcast/multicast
• Database replication
• Video streaming
• RSS feeds
• ...

Possible Solutions
Flooding
• Robust, but ineﬃcient (O(n2
))

Possible Solutions
Flooding
))
Tree
• Eﬃcient (O(n)), but fragile

Possible Solutions
Flooding
))
Tree
• Eﬃcient (O(n)), but fragile
Gossip
• Eﬃcient (O(nlogn)) and robust, but has relative high latency

Epidemic/Gossip Algorithms

Introduction
Epidemiology studies the spread of a disease or infection in terms
of populations of infected/uninfected individuals and their rates of
change.

Introduction
change.
Nodes infect each other trough messages.
Total number of messages is less than O(n2).
No node is overloaded.

Introduction
change.
Nodes infect each other trough messages.
Total number of messages is less than O(n2).
No node is overloaded.
But
• No deterministic guarantee on reliability.
• Only probabilistic ones.

History of the Epidemic/Gossip Paradigm
First deﬁned by Alan Demers et al. (1987)
90s: gossip applied to the information dissemination problem
00s: gossip beyond dissemination
2006: Workshop on the future of gossip (Leiden, the Netherlands)

History of the Epidemic/Gossip Paradigm (1987)
Database replicated at thousands of nodes.

Heterogeneous and unreliable network.

Independent updates to single elements of the DB are injected at
multiple nodes.

multiple nodes.
Updates must propagate to all nodes or be supplanted by later up-
dates of the same element.

multiple nodes.
Updates must propagate to all nodes or be supplanted by later up-
dates of the same element.
Replicas become consistent after no more new updates.

History of the Epidemic/Gossip Paradigm (Today)
Amazon uses a gossip protocol to quickly spread information
throughout the S3 system.
Amazon’s Dynamo uses a gossip-based failure detection service.
The basic information exchange in BitTorrent is based on gossip.

SIR Model (1/2)
Kermack and McKendrick, 1927
An individual p can be:
• Susceptible: if p is not yet infected by the disease.
• Infective: if p is infected and capable to spread the disease.
• Removed: if p has been infected and has recovered from the disease.

SIR Model (2/2)
Initially, a single individual is infective.
Individuals get in touch with each other, spreading the disease.
Susceptible individuals are turned into infective ones.
Eventually, infective individuals will become removed.

From Epidemiology to Distributed Systems
The idea
• Disease spread quickly and robustly.
• Our goal is to spread an update as fast and as reliable as possible.
• Can we apply these ideas to distributed systems?

From Epidemiology to Distributed Systems
The idea
• Disease spread quickly and robustly.
• Our goal is to spread an update as fast and as reliable as possible.
• Can we apply these ideas to distributed systems?
SIR Model for database replication:
• Susceptible: if p has not yet received an update.
• Infective: if p has not yet received an update.
• Removed: if p has the update but is no longer willing to share it.

Two Styles of Epidemic Protocols
Anti-entropy
Rumor mongering

Anti-Entropy
Each node p periodically contacts a random partner q selected from
the current population.

Anti-Entropy
Each node p periodically contacts a random partner q selected from
the current population.
Then, p and q engage in an information exchange protocol, where
updates known to p but not to q are transferred from p to q (push),
or vice-versa (pull), or in both direction (push-pull).

Rumor Mongering
Nodes are initially ignorant.

Rumor Mongering
When an update is learned by a node, it becomes a hot rumor.

Rumor Mongering
While a node holds a hot rumor, it periodically chooses a random
node from the current population and sends (pushes) the rumor to
it.

Rumor Mongering
While a node holds a hot rumor, it periodically chooses a random
node from the current population and sends (pushes) the rumor to
it.
Eventually, a node will lose interest in spreading the rumor.

Epidemic Algorithms Applications
Aggregation
Peer sampling (Cyclon)
Topology management (Tman)
...

Aggregation

Aggregation
Aggregation provides a summary of some global system property.

Aggregation
It allows local access to global information.

Aggregation
It allows local access to global information.
Examples of aggregation functions:
• The average load of nodes in a cluster.
• The sum of free space in a distributed storage.
• The total number of nodes in a P2P system.

Aggregation Generic Framework (1/3)
Executed by all processes:
repeat evert t time units:
q = selectRandomPeer() // Select a random neighbor
send <p, pullRequest, Sp> to q

upon receive<p, pullRequest, Sp> do:
send <q, pullResponse, Sq> to p
Sq = update(Sp, Sq)

upon receive<p, pullRequest, Sp> do:
send <q, pullResponse, Sq> to p
Sq = update(Sp, Sq)
update function:
• avg: return (Sp + Sq) / 2
• max: return max(Sp, Sq)

upon receive<q, pullResponse, Sq> do:
Sp = update(Sp, Sq)

upon receive<q, pullResponse, Sq> do:
Sp = update(Sp, Sq)
update function:
• avg: return (Sp + Sq) / 2
• max: return max(Sp, Sq)

Aggregation Example (1/5)
Taking the average of the numbers in the nodes.

Network Size Estimation
Any ideas?

Any ideas?
All nodes set their states to 0.

Any ideas?
The initiator sets its state to 1 and starts gossiping for the average.

Any ideas?
The initiator sets its state to 1 and starts gossiping for the average.
Eventually all nodes converge to the avg = 1
N .

Peer Sampling Service

Epidemic Protocols
In a epidemic (gossip) protocol, each node in the system periodically
exchanges information with a subset of nodes.

Epidemic Protocols
The choice of this subset is crucial.

Epidemic Protocols
The choice of this subset is crucial.
Ideally, the nodes should be selected following a uniform random
sample of all nodes currently in the system.

Achieving a Uniform Random Sample
Each node may be assumed to know every other node in the system.

Achieving a Uniform Random Sample
Each node may be assumed to know every other node in the system.
Providing each node with a complete membership table is unrealistic
in a large scale dynamic system.

Peer Sampling
An alternative solution.

Peer Sampling
Every node maintains a relatively small local membership table that
provides a partial view on the complete set of nodes.

Peer Sampling
Every node maintains a relatively small local membership table that
provides a partial view on the complete set of nodes.
Periodically refreshes the table using a gossiping procedure.

Peer Sampling Generic Framework (1/4)
q = selectPeer()
buf = ((myAddress, 0))
view.permute()
move oldest H items to the end of view
buf.append(view.head(c/2-1))
send <p, psRequest, buf> to q

upon receive<p, psRequest, bufp> do:
buf = ((myAddress, 0))
view.permute()
move oldest H items to the end of view
buf.append(view.head(c/2-1))
send <q, psResponse, buf> to p
view.select(c, H, S, bufp)
view.increaseAge()

upon receive<q, psResponse, bufq> do:
view.select(c, H, S, bufq)
view.increaseAge()

method view.select(c, H, S, bufp)
view.append(bufp)
view.removeDuplicates()
view.removeOldItems(min(H, view.size-c))
view.removeHead(min(S, view.size-c))
view.removeAtRandom(view.size-c)

Gossip-based Peer Sampling (1/7)

Peer Sampling Design Space
Peer Selection
• Rand: uniform random
• Tail: highest age
View Propagation
• Push
• Push-Pull
View Selection
• Blind: H = 0, S = 0
• Healer: H = c/2
• Swapper: H = 0, S = c/2

Cyclon as a Peer Sampling Service
Peer Selection
• Rand: uniform random
• Tail: highest age
View Propagation
• Push
• Push-Pull
View Selection
• Blind: H = 0, S = 0
• Healer: H = c/2
• Swapper: H = 0, S = c/2

Cyclon (1/5)

Cyclon (2/5)
Pick the oldest node from my view and remove it from the view
(tail)

Cyclon (3/5)
Exchange some of the nodes in neighbours (push-pull)

Cyclon (4/5)
Exchange some of the nodes in neighbours (push-pull)

Cyclon (5/5)
Update the views (swapper)

Topology Management

T-Man
T-man is a protocol to construct and maintain any topology with
the help of a ranking function.

T-Man
T-man is a protocol to construct and maintain any topology with
the help of a ranking function.
The ranking function orders any set of nodes according to their
desirability to be neighbors of a given node.

T-Man Generic Framework (1/3)
Executed by all processes.
q = selectPeer()
myDescriptor = (myAddress, myProfile)
buf = merge(view, myDescriptor)
buf = merge(buf, view.rnd)
send <p, tmanRequest, buf> to q

q = selectPeer()
selectPeer
• Sort all nodes in the view based on ranking.
• Pick randomly one node from the ﬁrst half.

q = selectPeer()
selectPeer
• Sort all nodes in the view based on ranking.
• Pick randomly one node from the ﬁrst half.
view.rnd
• Provides a random sample of the nodes from the entire network,
e.g., using cyclon.

buf = merge(buf, rnd.view)
send <q, tmanResponse, buf> to p
buf = merge(bufp, view)
view = selectView(buf)

buf = merge(buf, rnd.view)
send <q, tmanResponse, buf> to p
buf = merge(bufp, view)
selectView
• Sort all nodes in buﬀer (about double size of the view).
• Pick out c highest ranked nodes.

upon receive<q, tmanResponse, bufq> do:
buf = merge(bufq, view)

upon receive<q, tmanResponse, bufq> do:
buf = merge(bufq, view)
selectView
• Sort all nodes in buﬀer (about double size of the view).
• Pick out c highest ranked nodes.

Ranking Function
Sample ranking functions:
• Line: d(a, b) = |a − b|
• Ring: d(a, b) = min(N − |a − b|, |a − b|)

Illustration of T-Man

Summary

Summary
Epidemic/Gossip algorithms: anti-entropy and rumor mongering
Aggregation
Peer sampling service: cyclon
• Peer selection
• View propagation
• View selection
Topology management: T-man

References:
M. Jelasity, and A. Montresor, Epidemic-style proactive aggregation
in large overlay networks, ICDCS, 2004.
M. Jelasity, and O. Babaoglu, T-Man: Gossip-based overlay topol-
ogy management, Engineering Self-Organising Systems, 2006.
M. Jelasity et al., Gossip-based peer sampling, TOCS, 2007.
S. Voulgaris, D. Gavidia, and M. Van Steen, Cyclon: Inexpensive
membership management for unstructured P2P overlays, Journal of
Network and Systems Management, 2005.
A. Demers et al., Epidemic algorithms for replicated database main-
tenance, PODC, 1987.

Questions?
Acknowledgements
Some slides were derived from Alberto Montresor (Trento University).

Gossip-based algorithms

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