Fence Patrolling by Mobile Agents with Distinct Speeds

  • Akitoshi Kawamura
  • Yusuke Kobayashi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)


Suppose we want to patrol a fence (line segment) using k mobile agents with 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 + … + 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 ≤ 3.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Akitoshi Kawamura
    • 1
  • Yusuke Kobayashi
    • 1
  1. 1.University of TokyoTokyoJapan

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