Round Robin Is Optimal for Fault-Tolerant Broadcasting on Wireless Networks

Abstract

We study the completion time of broadcast operations on Static Ad-Hoc Wireless Networks in presence of unpredictable and dynamical faults. As for oblivious fault-tolerant distributed protocols, we provide an Ω(Dn) lower bound where n is the number of nodes of the network and D is the source eccentricity in the fault-free part of the network. Rather surprisingly, this lower bound implies that the simple Round-Robin protocol, working in O(Dn) time, is an optimal fault-tolerant oblivious protocol. Then, we demonstrate that networks of o(n/ log n) maximum in-degree admit faster oblivious protocols. Indeed, we derive an oblivious protocol having O(D minn, Δ log n) completion time on any network of maximum in-degree Δ. Finally, we address the question whether adaptive protocols can be faster than oblivious ones. We show that the answer is negative at least in the general setting: we indeed prove an Ω(Dn) lower bound when $D = \Theta \left( {\sqrt n } \right)$. This clearly implies that no (adaptive) protocol can achieve, in general, o(Dn) completion time.

Research partially supported by the Italian MURST Project “REACTION” and the EC RTN Project “ARACNE”.