A New Algorithm for Construction of a P2P Multicast Hybrid Overlay Tree Based on Topological Distances

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.

A Note on Ultrametric Spaces, Minimum Spanning Trees and the Topological Distance Algorithm

“…Our contributions and motivations are threefold. First, our approach generalizes results of [1] to arbitrary metrics satisfying the axioms of ultrametric spaces. To the best of our knowledge, the connection between the topological distance algorithm, ultrametric spaces, and the abstract, discrete mathematics of matroids and greedoids has not been published before and hopefully some practitioners might find our remarks useful or appealing at the least.…”

“…It is also stable; i.e., a vertex added to the tree is never rearranged later. This is important for the network applications considered in [1,2,7] as it allows for dynamically constructing an optimal overlay network for, e.g., video conference participants with minimal modifications of the overlay network when new participants join.…”

“…To the best of our knowledge, the connection between the topological distance algorithm, ultrametric spaces, and the abstract, discrete mathematics of matroids and greedoids has not been published before and hopefully some practitioners might find our remarks useful or appealing at the least. Secondly, our approach yields simpler and more elegant proofs of some of the results proven in [1] and enables extensions of the algorithms presented therein. And thirdly, even if the metric involved does not possess the properties of an ultrametric, our results can nonetheless be useful for practical applications, as often the relevant metrics are close to an ultrametric.…”

“…Our motivation stems from algorithms for peer-to-peer network applications, as considered in [1,2]. In these papers a simple distance called topological distance based on IP-addresses has been introduced along with a greedy topological distance algorithm to compute (spanning) trees with minimum weight measured by this distance.…”

Evaluation of a Topological Distance Algorithm for Construction of a P2P Multicast Hybrid Overlay Tree

“…• Signaling and connection state events as described in [26] • Geolocation and the available bandwidth information about peers • Topological network coordinates according the definition in [27] • The p2p overlay topology as a graph • Sent/received and lost packets by each peer Peer Degree (PD) is the number of incoming and outgoing links. Peer Stretch (PS) is the ratio between the length of the data path from the server to a peer in our multicast tree to the length of the shortest path between them in the underlying network.…”