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The Computational Power of Beeps

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Distributed Computing (DISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9363))

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Abstract

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.

S. Gilbert—Supported in part by NUS FRC T1-251RES1404.

C. Newport—Supported in part by NSF grant CCF 1320279.

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Author information

Authors and Affiliations

  1. National University of Singapore, Singapore, Singapore

    Seth Gilbert

  2. Georgetown University, Washington, D.C, USA

    Calvin Newport

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  1. Seth Gilbert
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  2. Calvin Newport
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Corresponding author

Correspondence to Calvin Newport .

Editor information

Editors and Affiliations

  1. Technion, Haifa, Israel

    Yoram Moses

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Gilbert, S., Newport, C. (2015). The Computational Power of Beeps. In: Moses, Y. (eds) Distributed Computing. DISC 2015. Lecture Notes in Computer Science(), vol 9363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48653-5_3

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  • DOI: https://doi.org/10.1007/978-3-662-48653-5_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48652-8

  • Online ISBN: 978-3-662-48653-5

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