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International Colloquium on Structural Information and Communication Complexity

SIROCCO 2011: Structural Information and Communication Complexity pp 198–209Cite as

Improving the Optimal Bounds for Black Hole Search in Rings

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6796))

Abstract

In this paper we re-examine the well known problem of asynchronous black hole search in a ring. It is well known that at least 2 agents are needed and the total number of agents’ moves is at least Ω(n logn); solutions indeed exist that allow a team of two agents to locate the black hole with the asymptotically optimal cost of Θ(n logn) moves.

In this paper we first of all determine the exact move complexity of black hole search in an asynchronous ring. In fact, we prove that 3nlog3 n − O(n) moves are necessary. We then present a novel algorithm that allows two agents to locate the black hole with at most 3nlog3 n + O(n) moves, improving the existing upper bounds, and matching the lower bound up to the constant of proportionality. Finally we show how to modify the protocol so to achieve asymptotically optimal time complexity Θ(n), still with 3nlog3 n + O(n) moves; this improves upon all existing time-optimal protocols, which require O(n 2) moves. This protocol is the first that is optimal with respect to all three complexity measures: size (number of agents), cost (number of moves) and time; in particular, its cost and size complexities match the lower bounds up to the constant.

This work has been partially supported by NSERC Discovery program and by Dr. Flocchini’s University Research Chair.

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Author information

Authors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Balasingham Balamohan & Paola Flocchini

  2. Ryerson University, Toronto, Canada

    Ali Miri

  3. Carleton University, Ottawa, Canada

    Nicola Santoro

Authors
  1. Balasingham Balamohan
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  2. Paola Flocchini
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  3. Ali Miri
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  4. Nicola Santoro
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Editor information

Editors and Affiliations

  1. INRIA, Bordeau Sud-Ouest Research Center, 351 cours de la Libération, 33400, Talence cedex, France

    Adrian Kosowski

  2. Department of Computer Science and Communication Engineering, Kyushu University, 744, Motooka, 819-0395, Fukuoka, Japan

    Masafumi Yamashita

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Balamohan, B., Flocchini, P., Miri, A., Santoro, N. (2011). Improving the Optimal Bounds for Black Hole Search in Rings. In: Kosowski, A., Yamashita, M. (eds) Structural Information and Communication Complexity. SIROCCO 2011. Lecture Notes in Computer Science, vol 6796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22212-2_18

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  • DOI: https://doi.org/10.1007/978-3-642-22212-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22211-5

  • Online ISBN: 978-3-642-22212-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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