Robust Leader Election in a Fast-Changing World

John Augustine
(Indian Institute of Technology Madras)
Tejas Kulkarni
(Indian Institute of Technology Madras)
Paresh Nakhe
(Indian Institute of Technology Madras)
Peter Robinson
(Nanyang Technological University)

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 Ω(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.

In Keren Censor-Hillel and Valerie King: Proceedings Ninth International Workshop on Foundations of Mobile Computing (FOMC 2013), Jerusalem, Israel, October 17-18, 2013, Electronic Proceedings in Theoretical Computer Science 132, pp. 38–49.
Published: 17th October 2013.

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