Feasibility and complexity of broadcasting with random transmission failures

• Authors: Andrzej Pelc;David Peleg
• Venue: Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
• Year: 2005

We consider fault-tolerant broadcasting in the message passing and radio models under a probabilistic failure model. At each step, the transmitter of each node may fail independently with fixed probability p. We study both omission and Byzantine transmission failures. Our goal is to establish conditions on feasibility and to estimate the complexity of almost-safe broadcasting (i.e., broadcasting which is correct with probability at least 1-1/n on n-node graphs for sufficiently large n) under these scenarios. If only omission failures are assumed, almost-safe broadcasting is feasible for any p, in both communication models. For Byzantine faults, almost-safe broadcasting is feasible in the message passing model iff p and in the radio model iff pΔ+1, where Δ is the maximum degree of the network. For the time complexity of almost-safe broadcasting, we give the following upper and lower bounds. Consider an n-node graph G with a given source s, and denote by D the radius of G w.r.t. s (namely, the largest distance from s to any node in G). Then for the message passing model we show that assuming omission faults, the optimal almost-safe broadcasting time is Θ (D + log n). Assuming Byzantine faults, almost-safe broadcasting is possible in time O(D+log α n), for any constant α 1. For the radio model we show that almost-safe broadcasting in time O (opt + log n) (where opt is the optimal fault-free broadcasting time) is impossible for some graphs, even with omission failures, and we give an almost-safe broadcasting algorithm of time O(opt • log n) for any graph, for both types of failures.