A NEW ALGORITHM FOR CONSTRUCTION OF A P2P MULTICAST HYBRID OVERLAY TREE BASED ON TOPOLOGICAL DISTANCES

Jan Zizka et al. (Eds) : CCSIT, SIPP, AISC, CMCA, SEAS, CSITEC, DaKM, PDCTA, NeCoM - 2016
pp. 307–321, 2016. © CS & IT-CSCP 2016 DOI : 10.5121/csit.2016.60126
A NEW ALGORITHM FOR CONSTRUCTION OF
A P2P MULTICAST HYBRID OVERLAY TREE
BASED ON TOPOLOGICAL DISTANCES
Sergej Alekseev1
and Jörg Schäfer2
1
Department of Computer Science and Engineering, Computer Networks and OS,
Frankfurt University of Applied Sciences, Germany
alekseevf@fb2.fra-uas.de
2
Department of Computer Science and Engineering, Distributed Systems,
Frankfurt University of Applied Sciences, Germany
jschaefer@fb2.fra-uas.de
ABSTRACT
In the last decade Peer to Peer technology has been thoroughly explored, because it overcomes many
limitations compared to the traditional client server paradigm. Despite its advantages over a traditional
approach, the ubiquitous availability of high speed, high bandwidth and low latency networks has
supported the traditional client-server paradigm. Recently, however, the surge of streaming services has
spawned renewed interest in Peer to Peer technologies. In addition, services like geolocation databases
and browser technologies like Web-RTC make a hybrid approach attractive.
In this paper we present algorithms for the construction and the maintenance of a hybrid P2P overlay
multicast tree based on topological distances. The essential idea of these algorithms is to build a multicast
tree by choosing neighbours close to each other. The topological distances can be easily obtained by the
browser using the geolocation API. Thus the implementation of algorithms can be done web-based in a
distributed manner.
We present proofs of our algorithms as well as practical results and evaluations.
KEYWORDS
Distributed algorithms, peer-to-peer (P2P), hybrid, overlay multicast tree, live streaming
1. INTRODUCTION
Peer-to-Peer (P2P) streaming has become more and more popular nowadays again after interest
in general P2P has generally decreased after the initial enthusiasm in the late 90 – partially due to
the ubiquitous and quick availability of high speed, high bandwidth and low latency networks
which has supported the traditional client-server paradigm in the last decade. The central strength
of P2P streaming systems is the capability of sharing resources so that larger (and more costly)
servers can be replaced by smaller (and cheaper) computers. The P2P networks are build usually
as a logical overlay network. The contribution of this paper is the construction and management
of a P2P multicast tree streaming overlay where the nodes are physically close to each other in

308 Computer Science & Information Technology (CS & IT)
the underlying network. In this paper we present two algorithms. The first is the joining algorithm
that each node runs when it enters the system. The essential idea of the algorithm is to construct a
multicast tree structure by finding a suitable neighbour in the overlay multicast tree and
considering resources of peers. The second algorithm handles a host leaving that occurs
gracefully or accidentally. For both algorithms we provide full mathematical proofs of minimality
features. In addition, we present some experimental results and evaluations. And finally we
conclude our paper with remarks on possible future work.
2. RELATED WORKS
In recent years a number of P2P-based applications for stream delivery have been developed –
e.g. Zattoo (http://zattoo.com), PPTP (http://www.pptv.com) and Octoshape (https: // octoshape.
com).
To improve the scalability and to optimise the usage of resources in the P2P network, several
approaches have been proposed. In [1] various problems that arise due to the fact of P2P systems
being highly dynamic and heterogenous are examined. It focuses especially on resilience
mechanisms. In [2] and [6] an overview of application and network layer mechanisms are
presented and the Mesh and Multiple-Tree P2P overlays are compared.
Several applications have been developed for various categories of mesh based P2P streaming.
The authors of [8] and [7] present a hybrid approach for overlay construction and data delivery in
an application-layer multicast. The HyPO approach in [7] optimizes the overlay by organizing
peers with similar bandwidth ranges in a geographical area into a mesh overlay. The ToMo
approach in [7] combines the strong points of a tree-based structure and a mesh-based data
delivery to a two-layer hybrid overlay. The mTreebone of [9] is a collaborative tree-mesh design
that leverages both mesh and tree structures. The key idea is to identify a set of stable nodes to
construct a tree-based backbone with most of the data being pushed over this backbone. AnySee
[5] is a mesh based P2P system in which resources are assigned based on their locality and delay.
In the present work we propose algorithms to construct a tree based multicast overlay based on
topological distances. Similar approaches are described in [12], [3] and [14]. Already in [20] an
architecture has been proposed for designing a global internet host distance estimation service.
However, only relatively recently geographical information has become practically available
from freely available geolocation databases [16], and therefore ideas which have been of
theoretical value only have now become practical, see also [19]. The approach used in [12] and
[3] organizes the peers into a hierarchy of clusters such that the neighboring peers are grouped
into the same cluster. The overlay network is build from the cluster leaders to the other members
recursively. In [14] a locality-aware P2P overlay construction method, called Nearcast, is
proposed which builds an efficient overlay multicast tree by letting each peer node choose
physically closer nodes as its logical children. Whereas there is rather comprehensive coverage of
theoretical P2P algorithms and mathematical theorems on some of them like e.g. the T-Man
protocol, see [4], up to our best knowledge, no minimality results have been proven for the
overlay networks like the one described above but rather simulation results have been computed.
In our work we propose algorithms which minimise the routing costs, usage of peer resources and
end-to-end delay based on the topological location of peers. We provide a proof for the
minimality of routing costs and provide evidence for keeping end-to-end delay low.

Computer Science & Information Technology (CS & IT) 309
3. PROPOSED APPROACH
The concept of P2P multicasting [11], [12] is often applied to reduce the costs needed to deploy
and to maintain services related to streaming of various content to many users, e.g. VoD, IPTV,
radio, news channels, etc. In this paper, we propose an approach to the construction of a P2P
overlay multicast tree with the goal to solve the following important problems:
– Optimal routing between peers: Transmission at an overlay P2P-network might be
inefficient, especially when the P2P-network is randomly constructed. This stems from the fact
that the distance between peers physically or topologically is not considered by constructing the
P2P-network.
– Optimal usage of peer resources: Peer resources include available bandwidth, processing
power and storage space.
– End-to-End delay: The end-to-end delay is the latency, accumulated peer by peer, for the
delivery of a data packet along the overlay path from the source host to an end host. To reduce
this delay the height of the multicast tree should be kept small.
– Handling of peer connections: In practice the P2P-network need to deal with peers joining the
network and peers that leave voluntarily or due to failure.
Figure 1. Topological search tree and p2p multicast tree structure.
To overcome these problems, we propose algorithms for the construction and the management of
an overlay P2P-network. Our algorithms use the topological distances between peers to guarantee
the optimal routing costs. We define two data structures, a topological search tree and a P2P
multicast tree (fig. 1). The search tree is used to find the nearest peer to be attached to the
multicast overlay. This a special case of the Nearest Neighbour Search (NNS) or closest point
search problem. Donald Knuth named this problem the post office problem [10]. The problem
relates to an application of the assignment to the next post office. In our case the problem is
reduced to the search in the tree and adapted for the search of an optimal usage of peer resources.
The P2P multicast tree is used for the actual data transfer.

4. P2P OVERLAY MULTICAST TREE CONSTRUCTION AND MAIN-
TENANCE
4.1. Definitions and Preliminaries
To identify the topological position of hosts in a network, a unique H-dimensional coordinate C
is assigned to each host. The idea to use the network coordinates is based on considerations from
[13], [14] and [15]. In contrast to the algorithms presented therein, we use in our approach two
data structures: the search tree Ts for searching the nearest neighbour according the topological
position in the network and the multicast tree T to connect hosts to a P2P overlay multicast
network.
The multicast overlay tree is defined as T = (V, E), where V is a set of vertices, which represent
the end hosts, and E is a set of directed edges, which represent data delivery streams between the
end hosts.

4.2. Joining algorithm
To construct a multicast overlay tree the joining algorithm connects the hosts to an overlay
network by analysing the geolocation information provided by the end hosts. The algorithm can
be implemented in a centralized or a distributed manner. The pseudocode of the joining algorithm
is shown in fig. 2.
Figure 2. The pseudocode of the JOIN algorithm
Figure 3 illustrates an example of the joining nodes to an existing overlay network. Initially the
overlay multicast tree contains only a source host S and the search tree Ts includes the
coordinates C(S) (fig. 3a). To attach the new node v1 the joining algorithm extends the search tree
Ts by the adding the coordinates C(v1) and determines the nearest host by traversing the search
tree Ts. The nearest neighbour can be easily found by a simple tree traversing in O(log n) time.
The new host v1 is attached to the host S (fig. 3b). The fig. 3c illustrates the attaching of the host
v2 to the multicast overlay tree.

Figure 3. An example of the algorithm JOIN execution.
Figure 4. Proof by induction

Figure 5. Topological distances

4.3 Management of peer-resources
Figure 6. The pseudocode of the JOINR algorithm

Figure 7. An example of the algorithm JOINR execution

Figure 8. Proof of the second loop.

4.4 End-to-End Delay

Figure 9. The pseudocode of the JOINRE algorithm
4.5 Reconstruction algorithm
5. EXPERIMENTAL EVALUATIONS

Figure 10. The pseudocode of the reconstruction algorithm

Figure 11. Comparison of results: JOIN - proposed algorithm, BBT - Balanced Binary Tree
6. CONCLUSION
In this paper we presented a novel multicast tree construction and maintenance approach based on
the topological network coordinates of the end hosts. The algorithms presented in this paper were
developed to achieve the following desirable properties:
– Minimal routing overhead in the underlying network
– Optimal resource management of the hosts
– Short end-to-end delay
We evaluated our approach theoretically and by using simulations. Compared to the randomly
generated trees our approach improves significantly the performance metrics of a multicast
overlay tree. Our future work will concentrate on implementing this approach in a real
environment, collecting and analysing the performance data.
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A NEW ALGORITHM FOR CONSTRUCTION OF A P2P MULTICAST HYBRID OVERLAY TREE BASED ON TOPOLOGICAL DISTANCES

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