Robust Leader Election in a Fast-Changing World

TL;DR

This paper introduces a randomized algorithm for leader election in highly dynamic networks, achieving near-optimal time complexity and applicable to wireless ad-hoc networks with adversarial node changes.

Contribution

It presents a novel randomized Las Vegas algorithm that elects a leader in O(D log n) rounds in dynamic networks, improving upon previous deterministic solutions.

Findings

Algorithm elects leader in O(D log n) rounds with high probability.

Proves lower bound of omega(D log n) rounds for randomized algorithms.

Applicable to wireless ad-hoc networks with broadcast constraints.

Abstract

We consider the problem of electing a leader among nodes in a highly dynamic network where the adversary has unbounded capacity to insert and remove nodes (including the leader) from the network and change connectivity at will. We present a randomized Las Vegas algorithm that (re)elects a leader in O(D\log n) rounds with high probability, where D is a bound on the dynamic diameter of the network and n is the maximum number of nodes in the network at any point in time. We assume a model of broadcast-based communication where a node can send only 1 message of O(\log n) bits per round and is not aware of the receivers in advance. Thus, our results also apply to mobile wireless ad-hoc networks, improving over the optimal (for deterministic algorithms) O(Dn) solution presented at FOMC 2011. We show that our algorithm is optimal by proving that any randomized Las Vegas algorithm takes at least omega(D\log n) rounds to elect a leader with high probability, which shows that our algorithm yields the best possible (up to constants) termination time.