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Optimal Message-Passing with Noisy Beeps

Davies-Peck, Peter

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Abstract

Beeping models are models for networks of weak devices, such as sensor networks or biological networks. In these networks, nodes are allowed to communicate only via emitting beeps: unary pulses of energy. Listening nodes have only the capability of carrier sensing: they can only distinguish between the presence or absence of a beep, but receive no other information. The noisy beeping model further assumes listening nodes may be disrupted by random noise. Despite this extremely restrictive communication model, it transpires that complex distributed tasks can still be performed by such networks. In this paper we provide an optimal procedure for simulating general message passing in the beeping and noisy beeping models. We show that a round of Broadcast CONGEST can be simulated in O(∆ log n) rounds of the noisy (or noiseless) beeping model, and a round of CONGEST can be simulated in O(∆ 2 log n) rounds (where ∆ is the maximum degree of the network). We also prove lower bounds demonstrating that no simulation can use asymptotically fewer rounds. This allows a host of graph algorithms to be efficiently implemented in beeping models. We present several example applications, including an O(log n)-round Broadcast CONGEST algorithm for maximal matching, which, when simulated using our method, immediately implies a near-optimal O(∆ log 2 n)-round maximal matching algorithm in the noisy beeping model. A preliminary version of this paper appeared in the proceedings of the 2023 ACM Symposium on Principles of Distributed Computing (PODC) [14].

Citation

Davies-Peck, P. (online). Optimal Message-Passing with Noisy Beeps. Distributed Computing,

Journal Article Type Article
Acceptance Date May 27, 2025
Online Publication Date Jun 10, 2025
Deposit Date Jun 5, 2025
Publicly Available Date Jun 17, 2025
Journal Distributed Computing
Print ISSN 0178-2770
Electronic ISSN 1432-0452
Publisher Springer
Peer Reviewed Peer Reviewed
Keywords Message Passing; Beeping Model; Superimposed Codes
Public URL https://durham-repository.worktribe.com/output/4089497

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