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. Concerning 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 min{n,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=Θ( n ) . This clearly implies that no ( adaptive) protocol can achieve, in general, o( Dn) completion time.