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Fast Searching on Cartesian Products of Graphs

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Theory and Applications of Models of Computation (TAMC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10185))

Abstract

Given a graph that contains an invisible fugitive, the fast searching problem is to find the fast search number, i.e., the minimum number of searchers to capture the fugitive in the fast search model. In this paper, we give a new lower bound on the fast search number. Using the new lower bound, we prove an explicit formula for the fast search number of the Cartesian product of an Eulerian graph and a path. We also give formulas for the fast search number of variants of the Cartesian product. We present an upper bound and a lower bound on the fast search number of hypercubes, and extend the results to a broader class of graphs including toroidal grids.

B. Yang—Research supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-2013-261290.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada

    Yuan Xue & Boting Yang

Authors
  1. Yuan Xue
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  2. Boting Yang
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Corresponding author

Correspondence to Boting Yang .

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Editors and Affiliations

  1. Anna University, Chennai, India

    T.V. Gopal

  2. Universität Bern , Bern, Switzerland

    Gerhard Jäger

  3. Universität Bern , Bern, Switzerland

    Silvia Steila

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Xue, Y., Yang, B. (2017). Fast Searching on Cartesian Products of Graphs. In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_48

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  • DOI: https://doi.org/10.1007/978-3-319-55911-7_48

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55910-0

  • Online ISBN: 978-3-319-55911-7

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