Beeping a maximal independent set

Afek, Yehuda; Alon, Noga; Bar‐Joseph, Ziv; Cornejo, Alejandro; Haeupler, Bernhard; Kühn, Fabian

doi:10.1007/s00446-012-0175-7

Cited by 70 publications

(165 citation statements)

References 18 publications

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“…In this paper, we prove that the algorithmic complexity threshold for solving many useful problems is actually much lower: O(1) states are sufficient for high probability results and O(log (1/ǫ)) states are sufficient for fixed error bound results. 1 We argue the direction pursued in this paper (how complex must algorithms become to solve useful problems with beeps) complements the direction pursued in existing papers (how fast can algorithms solve useful problems with beeps). Answers to both types of queries is necessary to continue to understand the important topic of coordination in constrained network environments.…”

Section: Comparison To Existing Beep Resultsmentioning

confidence: 84%

“…If you assume receiver collision detection, these solutions require only polylogarithmic expected time. 2 These results violate our lower bounds for leader election with 1 Notice, direct comparisons between many of these results is complicated by the variety of possible assumptions; e.g., synchronous versus asynchronous starts, multihop versus single hop, small versus large probability precision. 2 For example: divide rounds into pairs of even and odd rounds.…”

Section: Comparison To Existing Beep Resultsmentioning

confidence: 88%

“…They argued that something like this algorithm might play a role in the proper distribution of sensory organ precursor cells in fruit fly nervous system development. Follow-up work [1,2,19] removed some of the stronger assumptions of [3] and improved the time complexity. In recent work, Förster et al [14] considered deterministic leader election in a multihop beeping network.…”

Section: Comparison To Existing Beep Resultsmentioning

confidence: 99%

“…The beeping model of network communication [1][2][3]10,14,19] assumes a collection of computational nodes, connected in a network, that interact by beeping in synchronous rounds. If a node decides to beep in a given round, it receives no feedback from the channel.…”

Section: Introductionmentioning

confidence: 99%

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The Computational Power of Beeps

Gilbert

Newport

2015

Lecture Notes in Computer Science

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In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by focusing on randomized leader election. We prove a lower bound on the states required to solve this problem with a given error bound, probability precision, and (when relevant) network size lower bound. We then show the bound tight with a matching upper bound. Noting that our optimal upper bound is slow, we describe two faster algorithms that trade some state optimality to gain efficiency. We then turn our attention to more general classes of problems by proving that once you have enough states to solve leader election with a given error bound, you have (within constant factors) enough states to simulate correctly, with this same error bound, a logspace TM with a constant number of unary input tapes: allowing you to solve a large and expressive set of problems. These results identify a key simplicity threshold beyond which useful distributed computation is possible in the beeping model.

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Section: Comparison To Existing Beep Resultsmentioning

confidence: 84%

Section: Comparison To Existing Beep Resultsmentioning

confidence: 88%

Section: Comparison To Existing Beep Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Computational Power of Beeps

Gilbert

Newport

2015

Lecture Notes in Computer Science

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“…It is easy to see that in general graphs, an independent set of size β(G) may be a factor Θ(n) smaller than the independence number α(G) 1 . This raises the following questions:…”

Section: Turán's Bound and A One-round Algorithmmentioning

confidence: 99%

Computing large independent sets in a single round

Halldórsson

Konrad

2017

Distrib. Comput.

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Independent sets play a central role in distributed algorithmics. We examine here the minimal requirements for computing non-trivial independent sets. In particular, we focus on algorithms that operate in a single communication round. A classic result of Linial shows that a constant number of rounds does not suffice to compute a maximal independent set. We are therefore interested in the size of the solution that can be computed, especially in comparison to the optimal. Our main result is a randomized one-round algorithm that achieves poly-logarithmic approximation on graphs of polynomially bounded-independence. Specifically, we show that the algorithm achieves the Caro-Wei bound (an extension of the Turán bound for independent sets) in general graphs up to a constant factor, and that the Caro-Wei bound yields a poly-logarithmic approximation on bounded-independence graphs. The algorithm uses only a single bit message and operates in a beeping model, where a node receives only the disjunction of the bits transmitted by its neighbors. We give limitation results that show that these are the minimal requirements for obtaining non-trivial solutions. In particular, a sublinear approximation cannot be obtained in a single round on general graphs, nor when nodes cannot both transmit and receive messages. We also show that our analysis of the Caro-Wei bound on polynomially bounded-independence graphs is tight, and that the poly-logarithmic approximation factor does not extend to O(1)-claw free graphs.

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Optimal Multi-broadcast with Beeps Using Group Testing

Beauquier

Burman

Davies

et al. 2019

Structural Information and Communication Complexity

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The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we obtain time-optimal and deterministic solutions for the fundamental communication task of multi-broadcast. The proposed solutions are completely uniform, i.e., independent of the network and problem parameters. The originality of our approach lies in the use of (combinatorial) group testing strategies, originally developed in the centralized context. We improve on previous solutions to multi-broadcast by giving efficiently constructible solutions, that is, with local computation cost polynomial in the identifiers' range.

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Beeping a maximal independent set

Cited by 70 publications

References 18 publications

The Computational Power of Beeps

The Computational Power of Beeps

Computing large independent sets in a single round

Optimal Multi-broadcast with Beeps Using Group Testing

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