Quasi-Optimal Leader Election Algorithms in Radio Networks with Loglogarithmic Awake Time Slots

TL;DR

This paper introduces two energy-efficient, randomized leader election algorithms for radio networks that operate in logarithmic expected time with minimal awake slots, matching known theoretical lower bounds.

Contribution

The paper presents two novel leader election protocols for radio networks that are energy-efficient and operate in optimal expected time, regardless of collision detection capabilities.

Findings

Both algorithms elect a leader in O(log n) expected time.

Stations remain awake for at most O(log log n) slots.

Algorithms match the established lower bound for leader election time.

Abstract

A radio network (RN) is a distributed system consisting of $n$ radio stations. We design and analyze two distributed leader election protocols in RN where the number $n$ of radio stations is unknown. The first algorithm runs under the assumption of {\it limited collision detection}, while the second assumes that {\it no collision detection} is available. By ``limited collision detection'', we mean that if exactly one station sends (broadcasts) a message, then all stations (including the transmitter) that are listening at this moment receive the sent message. By contrast, the second no-collision-detection algorithm assumes that a station cannot simultaneously send and listen signals. Moreover, both protocols allow the stations to keep asleep as long as possible, thus minimizing their awake time slots (such algorithms are called {\it energy-efficient}). Both randomized protocols in RN areshown to elect a leader in $O(\log{(n)})$ expected time, with no station being awake for more than $O(\log{\log{(n)}})$ time slots. Therefore, a new class of efficient algorithms is set up that match the $\Omega(\log{(n)})$ time lower-bound established by Kushilevitz and Mansour.