Compact Deterministic Self-Stabilizing Leader Election: The Exponential Advantage of Being Talkative

TL;DR

This paper introduces a deterministic self-stabilizing leader election protocol for rings that significantly reduces memory requirements from Omega(log n) to O(log log n) bits per node, without increasing stabilization time.

Contribution

It presents a novel non-silent protocol for leader election in rings with exponentially less memory than previous bounds, maintaining practical features.

Findings

Uses only O(log log n) memory bits per node.

Stabilizes in O(n log^2 n) rounds.

Works without knowing ring size or synchrony assumptions.

Abstract

This paper focuses on compact deterministic self-stabilizing solutions for the leader election problem. When the protocol is required to be \emph{silent} (i.e., when communication content remains fixed from some point in time during any execution), there exists a lower bound of Omega(\log n) bits of memory per node participating to the leader election (where n denotes the number of nodes in the system). This lower bound holds even in rings. We present a new deterministic (non-silent) self-stabilizing protocol for n-node rings that uses only O(\log\log n) memory bits per node, and stabilizes in O(n\log^2 n) rounds. Our protocol has several attractive features that make it suitable for practical purposes. First, the communication model fits with the model used by existing compilers for real networks. Second, the size of the ring (or any upper bound on this size) needs not to be known by any node. Third, the node identifiers can be of various sizes. Finally, no synchrony assumption, besides a weakly fair scheduler, is assumed. Therefore, our result shows that, perhaps surprisingly, trading silence for exponential improvement in term of memory space does not come at a high cost regarding stabilization time or minimal assumptions.