We are motivated by the problem of designing a simple distributed algorithm for Peer-to-Peer streaming applications that can achieve high throughput and low delay, while allowing the neighbor set maintained by each peer to be small. While previous works have mostly used tree structures, our algorithm constructs multiple random directed Hamiltonian cycles and disseminates content over the superposed graph of the cycles. We show that it is possible to achieve the maximum streaming capacity even when each peer only transmits to and receives from Theta(1) neighbors. Further, we show that the proposed algorithm achieves the streaming delay of Theta(log N) when the streaming rate is less than (1-1 K) of the maximum capacity for any fixed integer K>1, where N denotes the number of peers in the network. The key theoretical contribution is to characterize the distance between peers in a graph formed by the superposition of directed random Hamiltonian cycles, in which edges from one of the cycles may be dropped at random. We use Doob martingales and graph expansion ideas to characterize this distance as a function of N, with high probability.
Unstructured P2P networks overcome this vulnerability to peer churn. In unstructured P2P networks, peers find their neighboring peers randomly and get paired with them locally. As a neighboring peer leaves, a peer chooses another peer randomly as its new neighboring peer. Due to the distributed fashion of this peer pairing, unstructured P2P networks are robust to peer churn, unlike the structured P2P networks. However, the fundamental limitation of unstructured P2P networks is weak connectivity. Since peers are paired randomly without considering the entire network topology, there may be some peers that are not strongly connected from the source, which results in poor throughput and delay. To ensure full connectivity in this approach, it is required that every peer should be paired with @math neighboring peers @cite_17 , or should constantly change their neighbors to find neighbors providing a better streaming rate @cite_8 . However, in these approaches, delay performance is hard to guarantee because chunks have to be disseminated over an unknown'' network topology.
@cite_8 @cite_17
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Current peer-to-peer (P2P) systems often suffer from a large fraction of freeriders not contributing any resources to the network. Various mechanisms have been designed to overcome this problem. However, the selfish behavior of peers has aspects which go beyond resource sharing. This paper studies the effects on the topology of a P2P network if peers selfishly select the peers to connect to. In our model, a peer exploits locality properties in order to minimize the latency (or response times) of its lookup operations. At the same time, the peer aims at not having to maintain links to too many other peers in the system. By giving tight bounds on the price of anarchy, we show that the resulting topologies can be much worse than if peers collaborated. Moreover, the network may never stabilize, even in the absence of churn. Finally, we establish the complexity of Nash equilibria in our game theoretic model of P2P networks. Specifically, we prove that it is NP-hard to decide whether our game has a Nash equilibrium and can stabilize. We propose a novel search mechanism for unstructured p2p networks, and show that it is both scalable, i.e., it leads to a bounded query traffic load per peer as the peer population grows, and reliable, i.e., it successfully locates all files that are (sufficiently often) brought into the system. To the best of our knowledge, this is the first time that a search mechanism for unstructured p2p networks has been shown to be both scalable and reliable. We provide both a formal analysis and a numerical case study to illustrate this result. Our analysis is based on a random graph model for the overlay graph topology and uses a mean-field approximation to characterize the evolution of how files are replicated in the network. In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In the LOCAL model, this is quite simple: each node broadcasts all of its information in each round, and the number of rounds required will be equal to the diameter of the underlying communication graph. In the GOSSIP model, each node must independently choose a single neighbor to contact, and the lack of global information makes it difficult to make any sort of principled choice. As such, researchers have focused on the uniform gossip algorithm, in which each node independently selects a neighbor uniformly at random. When the graph is well-connected, this works quite well. In a string of beautiful papers, researchers proved a sequence of successively stronger bounds on the number of rounds required in terms of the conductance φ and graph size n, culminating in a bound of O(φ-1 log n). In this paper, we show that a fairly simple modification of the protocol gives an algorithm that solves the information dissemination problem in at most O(D + polylog (n)) rounds in a network of diameter D, with no dependence on the conductance. This is at most an additive polylogarithmic factor from the trivial lower bound of D, which applies even in the LOCAL model. In fact, we prove that something stronger is true: any algorithm that requires T rounds in the LOCAL model can be simulated in O(T + polylog(n)) rounds in the GOSSIP model. We thus prove that these two models of distributed computation are essentially equivalent. We propose a self-stabilizing and modeless peer-to-peer (P2P) network construction and maintenance protocol, called the Ring Network (RN) protocol. The RN protocol, when started on a network of peers that are in an arbitrary state, will cause the network to converge to a structured P2P system with a directed ring topology, where peers are ordered according to their identifiers. Furthermore, the RN protocol maintains this structure in the face of peer joins and departures. The RN protocol is a distributed and asynchronous message-passing protocol, which fits well the autonomous behavior of peers in a P2P system. The RN protocol requires only the existence of a bootstrapping system which is weakly connected. Peers do not need to be informed of any global network state, nor do they need to assist in repairing the network topology when they leave. We provide a proof of the self-stabilizing nature of the protocol, and experimentally measure the average cost (in time and number of messages) to achieve convergence.