Leader Election in Multi-Hop Radio Networks

TL;DR

This paper introduces new randomized leader election algorithms for multi-hop radio networks that are optimal in expected time and improve worst-case performance, applicable with or without collision detection.

Contribution

It presents a unified framework for leader election in radio networks, achieving optimal expected-time algorithms and enhancements in worst-case running time, even in weaker models.

Findings

Optimal expected-time leader election algorithms developed.

Improved worst-case running time in directed networks without collision detection.

Framework applicable in both collision detection and beep models.

Abstract

In this paper we present a framework for leader election in multi-hop radio networks which yield randomized leader election algorithms taking $O(\text{broadcasting time})$ in expectation, and another which yields algorithms taking fixed $O(\sqrt{\log n})$-times broadcasting time. Both succeed with high probability. We show how to implement these frameworks in radio networks without collision detection, and in networks with collision detection (in fact in the strictly weaker beep model). In doing so, we obtain the first optimal expected-time leader election algorithms in both settings, and also improve the worst-case running time in directed networks without collision detection by an $O(\sqrt {\log n})$ factor.