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Fence patrolling by mobile agents with distinct speeds

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Abstract

Suppose we want to patrol a fence (line segment) using \(k\) mobile agents with given speeds \(v _1\), ..., \(v _k\) so that every point on the fence is visited by an agent at least once in every unit time period. Czyzowicz et al. conjectured that the maximum length of the fence that can be patrolled is \((v _1 + \cdots + v _k)/2\), which is achieved by the simple strategy where each agent \(i\) moves back and forth in a segment of length \(v _i / 2\). We disprove this conjecture by a counterexample involving \(k = 6\) agents. We also show that the conjecture is true for \(k \le 3\).

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Acknowledgments

We thank Yoshio Okamoto for suggesting this research. We also thank Taisuke Izumi, Kohei Shimane, Yushi Uno and the anonymous referees for helpful comments.

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Authors and Affiliations

  1. University of Tokyo, Tokyo, Japan

    Akitoshi Kawamura & Yusuke Kobayashi

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  1. Akitoshi Kawamura
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  2. Yusuke Kobayashi
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Correspondence to Akitoshi Kawamura.

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A preliminary version of this paper was presented at the 23rd International Symposium on Algorithms and Computation [10]. Supported in part by KAKENHI (Grant-in-Aid for Scientific Research, Japan).

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Kawamura, A., Kobayashi, Y. Fence patrolling by mobile agents with distinct speeds. Distrib. Comput. 28, 147–154 (2015). https://doi.org/10.1007/s00446-014-0226-3

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  • DOI: https://doi.org/10.1007/s00446-014-0226-3

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