Exactly Optimal Deterministic Radio Broadcasting with Collision Detection

TL;DR

This paper presents a deterministic broadcasting algorithm in the beeping model with collision detection, matching the lower bound and showing that additional power in the model does not reduce round complexity.

Contribution

It introduces an optimal deterministic algorithm for radio broadcasting with collision detection and proves a matching lower bound, clarifying the model's limitations.

Findings

The algorithm improves round complexity over previous methods.

A matching lower bound proves optimality of the algorithm.

Additional power in the model does not reduce round complexity.

Abstract

We consider the broadcast problem in synchronous radio broadcast models with collision detection. One node of the network is given a message that must be learned by all nodes in the network. We provide a deterministic algorithm that works on the beeping model, which is a restricted version of the radio broadcast model with collision detection. This algorithm improves on the round complexity of previous algorithms. We prove an exactly matching lower bound in the radio broadcast model with collision detection. This shows that the extra power provided by the radio broadcast model with collision detection does not help improve the round complexity.