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Beeping Deterministic CONGEST Algorithms in Graphs

Authors Pawel Garncarek , Dariusz R. Kowalski , Shay Kutten , Miguel A. Mosteiro

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  • Theory of computation → Distributed algorithms
Keywords
  • Beeping Networks
  • CONGEST Networks
  • deterministic simulations
  • graph algorithms

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Abstract

Beeping Network (BN) is a popular graph-based model of wireless computation, which applies the OR operation to one-bit messages sent simultaneously by neighbors. It admits fast (polylogarithmic in the number of nodes n) randomized solutions to many graph problems, but all known deterministic algorithms for non-trivial graph problems are at least polynomial in the maximum node degree Δ.
We improve known results for deterministic algorithms by showing that this polynomial can be as low as Õ(Δ²). More precisely, we show how to simulate a single round of any CONGEST algorithm in any network in O(Δ² polylog n) beeping rounds, each accommodating at most one beep per node, even if the nodes intend to send different messages to different neighbors. This upper bound reduces polynomially the time for a deterministic simulation of CONGEST in a Beeping Network, comparing to the best known algorithms, and nearly matches the time obtained recently using randomization (up to a poly-logarithmic factor) as well as the lower bound. Specifically, any algorithm designed for the CONGEST networks can be run in BNs with O(Δ² polylog n) multiplicative overhead, e.g., we can now deterministically compute an MIS in any BN in O(Δ² polylog n) beeping rounds, improving the previous best Θ(Δ³)-round solution. For h-hop simulations, we prove a lower bound Ω(Δ^{h+1}), and we design a nearly matching algorithm that is able to "pipeline" the node-to-node information in a faster way than beeping layer-by-layer.

Cite As Get BibTex

Pawel Garncarek, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro. Beeping Deterministic CONGEST Algorithms in Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.20

Author Details

Pawel Garncarek
  • Institute of Computer Science, University of Wroclaw, Poland
Dariusz R. Kowalski
  • School of Computer & Cyber Sciences, Augusta University, GA, USA
Shay Kutten
  • Department of Data and Decision Sciences, Technion, Haifa, Israel
  • The Grand Technion Energy Program, Haifa, Israel
Miguel A. Mosteiro
  • Pace University, Computer Science Department, New York, NY, USA

Funding

  • Garncarek, Pawel: Supported by the National Science Center, Poland (NCN), grant 2020/39/B/ST6/03288.
  • Kutten, Shay: The work of this author was funded in part by grant 1346/22 from the Israeli Science Foundation. His research was carried out within the framework of the Grand Technion Energy Program (GTEP). A part of this work was done while with Fraunhofer SIT Darmstadt.
  • Mosteiro, Miguel A.: Partially supported by Pace SRC grant and Kenan Fund.

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