### Abstract

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.

Original language | English |
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Title of host publication | Algorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings |

Publisher | Springer Verlag |

Pages | 598-608 |

Number of pages | 11 |

ISBN (Print) | 9783642352607 |

DOIs | |

Publication status | Published - 2012 |

Event | 23rd International Symposium on Algorithms and Computation, ISAAC 2012 - Taipei, Taiwan, Province of China Duration: Dec 19 2012 → Dec 21 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7676 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 23rd International Symposium on Algorithms and Computation, ISAAC 2012 |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 12/19/12 → 12/21/12 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Kawamura, A., & Kobayashi, Y. (2012). Fence patrolling by mobile agents with distinct speeds. In

*Algorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings*(pp. 598-608). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7676 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-35261-4_62