Multi-Message Broadcast with Abstract MAC Layers and Unreliable Links

TL;DR

This paper investigates multi-message broadcast in wireless networks using abstract MAC layer models, analyzing bounds and proposing an improved algorithm under enhanced model assumptions.

Contribution

It introduces new bounds relating unreliable link structures to broadcast efficiency and develops a faster broadcast algorithm in an enhanced MAC model.

Findings

Efficiency depends on link structure and topology restrictions.

Lower bounds show limitations under geographic distance constraints.

Enhanced model enables significantly faster broadcast algorithms.

Abstract

We study the multi-message broadcast problem using abstract MAC layer models of wireless networks. These models capture the key guarantees of existing MAC layers while abstracting away low-level details such as signal propagation and contention. We begin by studying upper and lower bounds for this problem in a {\em standard abstract MAC layer model}---identifying an interesting dependence between the structure of unreliable links and achievable time complexity. In more detail, given a restriction that devices connected directly by an unreliable link are not too far from each other in the reliable link topology, we can (almost) match the efficiency of the reliable case. For the related restriction, however, that two devices connected by an unreliable link are not too far from each other in geographic distance, we prove a new lower bound that shows that this efficiency is impossible. We then investigate how much extra power must be added to the model to enable a new order of magnitude of efficiency. In more detail, we consider an {\em enhanced abstract MAC layer model} and present a new multi-message broadcast algorithm that (under certain natural assumptions) solves the problem in this model faster than any known solutions in an abstract MAC layer setting.