Latency Optimal Broadcasting in Noisy Wireless Mesh Networks

TL;DR

This paper introduces a new latency-optimal broadcasting algorithm for noisy wireless mesh networks that is robust to noise and faults, improving previous results and extending to multi-message scenarios.

Contribution

It presents the first asymptotically optimal, noise-robust broadcasting algorithm for single and multiple messages in wireless mesh networks, addressing open problems in the field.

Findings

Achieves $D+O( ext{log}^2 n)$ latency for single-message broadcasting.

Extends robustness to noisy models with improved bounds over prior work.

Provides a multi-message broadcasting algorithm with $O(D + k ext{log} n + ext{log}^2 n)$ complexity.

Abstract

In this paper, we adopt a new noisy wireless network model introduced very recently by Censor-Hillel et al. in [ACM PODC 2017, CHHZ17]. More specifically, for a given noise parameter $p\in [0,1],$ any sender has a probability of $p$ of transmitting noise or any receiver of a single transmission in its neighborhood has a probability $p$ of receiving noise. In this paper, we first propose a new asymptotically latency-optimal approximation algorithm (under faultless model) that can complete single-message broadcasting task in $D+O(\log^2 n)$ time units/rounds in any WMN of size $n,$ and diameter $D$. We then show this diameter-linear broadcasting algorithm remains robust under the noisy wireless network model and also improves the currently best known result in CHHZ17 by a $\Theta(\log\log n)$ factor. In this paper, we also further extend our robust single-message broadcasting algorithm to $k$ multi-message broadcasting scenario and show it can broadcast $k$ messages in $O(D+k\log n+\log^2 n)$ time rounds. This new robust multi-message broadcasting scheme is not only asymptotically optimal but also answers affirmatively the problem left open in CHHZ17 on the existence of an algorithm that is robust to sender and receiver faults and can broadcast $k$ messages in $O(D+k\log n + polylog(n))$ time rounds.