Communication Efficient Self-Stabilizing Leader Election (Full Version)

TL;DR

This paper introduces a randomized self-stabilizing leader election algorithm that significantly reduces communication overhead to near-linear messages, stabilizes quickly, and constructs a spanning tree in general graphs.

Contribution

It presents a novel, communication-efficient, randomized self-stabilizing leader election algorithm with improved message complexity and stabilization time.

Findings

Total messages sent till stabilization is  O(n)

Stabilization occurs in  O(n) rounds in expectation

Post-stabilization, only one message per round over the spanning tree

Abstract

This paper presents a randomized self-stabilizing algorithm that elects a leader $r$ in a general $n$-node undirected graph and constructs a spanning tree $T$ rooted at $r$. The algorithm works under the synchronous message passing network model, assuming that the nodes know a linear upper bound on $n$ and that each edge has a unique ID known to both its endpoints (or, alternatively, assuming the $KT_{1}$ model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of $\tilde{O} (n)$ messages, each of constant size, till stabilization, while stabilizing in $\tilde{O} (n)$ rounds, in expectation and with high probability. After stabilization, the algorithm sends at most one constant size message per round while communicating only over the ($n - 1$) edges of $T$. In all these aspects, the communication overhead of the new algorithm is far smaller than that of the existing (mostly deterministic) self-stabilizing leader election algorithms. The algorithm is relatively simple and relies mostly on known modules that are common in the fault free leader election literature; these modules are enhanced in various subtle ways in order to assemble them into a communication efficient self-stabilizing algorithm.