Distributed Computing

, Volume 28, Issue 2, pp 147–154 | Cite as

Fence patrolling by mobile agents with distinct speeds

Article

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 \(k \le 3\).

Keywords

Idle time Mobile robots Partition-based strategy 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of TokyoTokyoJapan

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