An Optimal Randomized Broadcasting Algorithm in Radio Networks with Collision Detection

TL;DR

This paper introduces an optimal randomized broadcasting algorithm for radio networks with collision detection, achieving the best possible time complexity and resolving a long-standing open problem in distributed computing.

Contribution

It presents the first optimal randomized broadcasting algorithm in radio networks with collision detection, matching the known lower bound.

Findings

Broadcasts a message in $O(D+ ext{log}^2 n)$ time slots with high probability.

The algorithm is proven to be optimal, matching the lower bound.

Resolves a decades-old open problem in the field.

Abstract

We present a randomized distributed algorithm that in radio networks with collision detection broadcasts a single message in $O(D+\log^2 n)$ time slots, with high probability. In view of the lower-bound $\Omega(D+\log^2 n)$, our algorithm is optimal in the considered model answering the decades-old question of Alon, Bar-Noy, Linial and Peleg [JCSS 1991].