Robust Leader Election in a Fast-Changing World

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.

💡 Research Summary

The paper addresses the problem of electing a unique leader in a highly dynamic network where nodes may be inserted, removed, or have their connections altered arbitrarily by an adversary. The authors adopt a synchronous, round‑based model in which each node can broadcast at most one O(log n)‑bit message per round to its current neighbors without prior knowledge of who they are. A key system parameter is the dynamic communication diameter D: if a node starts flooding a message at round r, every node that remains alive for the interval