Adversary Immune Leader Election in ad hoc Radio Networks

Abstract

Recently, efficient leader election algorithms for ad hoc radio networks with low time complexity and energy cost have been designed even for the no-collision detection, (no-CD), model. However, these algorithms are fragile in the sense that an adversary may disturb communication at low energy cost so that more than one station may regard itself as a leader. This is a severe fault since the leader election is intended to be a fundamental subroutine used to avoid collisions and to make it reliable.

It is impossible to make the leader election algorithm totally resistant – if an adversary is causing collisions all the time no message comes through. So we consider the case that an adversary has limited energy resources, as any other participant.

We present an approach that yields a randomized leader election algorithm for a single-hop no-CD radio network. The algorithm has time complexity O(log³ N) and energy cost $O(\sqrt{{\rm log}N})$. This is worse than the best algorithms constructed so far (O(logN) time and O(log^* N) energy cost), but succeeds in presence of an adversary with energy cost Θ(logN) with probability 1 - 2$^{\rm - \Omega(\sqrt{log N})}$. (The O(log^* N) energy cost algorithm can be attacked by an adversary with energy cost O(1).)

partially supported by KBN grant 7 T11C 032 20