Distributed Agreement in Dynamic Peer-to-Peer Networks

TL;DR

This paper presents fast randomized algorithms for distributed agreement in highly dynamic P2P networks, achieving high-probability consensus despite significant node churn within a small number of rounds.

Contribution

It introduces novel algorithms that guarantee stable agreement under high churn rates, even against adaptive adversaries, with polylogarithmic round complexity.

Findings

Achieves agreement in O(log^2 n) rounds under linear churn with oblivious adversaries.

Achieves agreement in O(log m log^3 n) rounds under sublinear churn with adaptive adversaries.

Requires only polylogarithmic bits per node per round for the oblivious adversary algorithm.

Abstract

Motivated by the need for robust and fast distributed computation in highly dynamic Peer-to-Peer (P2P) networks, we study algorithms for the fundamental distributed agreement problem. P2P networks are highly dynamic networks that experience heavy node {\em churn}. Our goal is to design fast algorithms (running in a small number of rounds) that guarantee, despite high node churn rate, that almost all nodes reach a stable agreement. Our main contributions are randomized distributed algorithms that guarantee {\em stable almost-everywhere agreement} with high probability even under high adversarial churn in a polylogarithmic number of rounds: 1. An $O(\log^2 n)$-round ($n$ is the stable network size) randomized algorithm that achieves almost-everywhere agreement with high probability under up to {\em linear} churn {\em per round} (i.e., $\epsilon n$, for some small constant $\epsilon > 0$), assuming that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm). Our algorithm requires only polylogarithmic in $n$ bits to be processed and sent (per round) by each node. 2. An $O(\log m\log^3 n)$-round randomized algorithm that achieves almost-everywhere agreement with high probability under up to $\epsilon \sqrt{n}$ churn per round (for some small $\epsilon > 0$), where $m$ is the size of the input value domain, that works even under an adaptive adversary (that also knows the past random choices made by the algorithm). This algorithm requires up to polynomial in $n$ bits (and up to $O(\log m)$ bits) to be processed and sent (per round) by each node.