The Adversarial Noise Threshold for Distributed Protocols

We consider the problem of implementing distributed protocols, despite adversarial channel errors, on synchronous-messaging networks with arbitrary topology. In our first result we show that any n-party T-round protocol on an undirected communication network G can be compiled into a robust simulation protocol on a sparse (O(n) edges) subnetwork so that the simulation tolerates an adversarial error rate of Ω 1 n ; the simulation has a round complexity of O m log n n T , where m is the number of edges in G. (So the simulation is work-preserving up to a log factor.) The adversary’s error rate is within a constant factor of optimal. Given the error rate, the round complexity blowup is within a factor of O(k log n) of optimal, where k is the edge connectivity of G. We also determine that the maximum tolerable error rate on directed communication networks is Θ(1/s) where s is the number of edges in a minimum equivalent digraph. Next we investigate adversarial per-edge error rates, whe...

• Type: Journal
• Year: 2016
• Where: SODA
• Authors: William M. Hoza, Leonard J. Schulman
• Keywords: Algorithms, SODA 2016