Real-Time Peer-to-Peer Streaming Over Multiple Random Hamiltonian Cycles

TL;DR

This paper proposes a distributed P2P streaming algorithm using multiple random Hamiltonian cycles, achieving high throughput and low delay with small neighbor sets, and provides theoretical analysis of peer distances in such networks.

Contribution

It introduces a novel P2P streaming method based on superposing multiple random Hamiltonian cycles, achieving near-optimal capacity with minimal neighbor connections, and analyzes peer distances using advanced probabilistic tools.

Findings

Achieves maximum streaming capacity with Theta(1) neighbors per peer.

Attains Theta(log N) streaming delay under certain rate conditions.

Provides theoretical characterization of peer distances in the superposed graph.

Abstract

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.