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

We study the completion time of broadcast operations on static ad hoc wireless networks in presence of unpredictable and dynamical faults. Concerning oblivious fault-tolerant distributed protocols, we provide an OðDnÞ 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 OðDnÞ time, is an optimal fault-tolerant oblivious protocol. Then, we demonstrate that networks of oðn=log nÞ maximum in-degree admit faster oblivious protocols. Indeed, we derive an oblivious protocol having OðD minfn;D log ngÞ completion time on any network of maximum in-degree D: 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 OðDnÞ lower bound when D 1⁄4 Yð ffiffiffi n p Þ: This clearly implies that no (adaptive) protocol can achieve, in general, oðDnÞ completion time. r 2003 Elsevier Inc. All rights reserved.