On the power of randomization in distributed algorithms in dynamic networks with adaptive adversaries

Abstract

This paper investigates the power of randomization in general distributed algorithms in dynamic networks where the network’s topology may evolve over time, as determined by some adaptive adversary. In such a context, randomization may help algorithms to better deal with i) “bad” inputs to the algorithm, and ii) evolving topologies generated by “bad” adaptive adversaries. We prove that randomness offers limited power to better deal with “bad” adaptive adversary. We define a simple notion of prophetic adversary for determining the evolving topologies. Such an adversary accurately predicts all randomness in the algorithm beforehand, and hence the randomness will be useless against “bad” prophetic adversaries. Given a randomized algorithm P whose time complexity satisfies some mild conditions, we prove that P can always be converted to a new algorithm Q with comparable time complexity, even when Q runs against prophetic adversaries. This implies that the benefit of P using randomness for dealing with the adaptive adversaries is limited.