### Abstract

Suppose we want to patrol a fence (line segment) using $$k$$k mobile agents with given speeds $$v _1$$v1,.., $$v _k$$vk 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 $$(v _1 + \cdots + v _k)/2$$(v1+⋯+vk)/2, which is achieved by the simple strategy where each agent $$i$$i moves back and forth in a segment of length $$v _i / 2$$vi/2. We disprove this conjecture by a counterexample involving $$k = 6$$k=6 agents. We also show that the conjecture is true for $$k \le 3$$k≤3.

Original language | English |
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Pages (from-to) | 147-154 |

Number of pages | 8 |

Journal | Distributed Computing |

Volume | 28 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Hardware and Architecture
- Computer Networks and Communications
- Computational Theory and Mathematics

### Cite this

*Distributed Computing*,

*28*(2), 147-154. https://doi.org/10.1007/s00446-014-0226-3

**Fence patrolling by mobile agents with distinct speeds.** / Kawamura, Akitoshi; Kobayashi, Yusuke.

Research output: Contribution to journal › Article

*Distributed Computing*, vol. 28, no. 2, pp. 147-154. https://doi.org/10.1007/s00446-014-0226-3

}

TY - JOUR

T1 - Fence patrolling by mobile agents with distinct speeds

AU - Kawamura, Akitoshi

AU - Kobayashi, Yusuke

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Suppose we want to patrol a fence (line segment) using $$k$$k mobile agents with given speeds $$v _1$$v1,.., $$v _k$$vk 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 $$(v _1 + \cdots + v _k)/2$$(v1+⋯+vk)/2, which is achieved by the simple strategy where each agent $$i$$i moves back and forth in a segment of length $$v _i / 2$$vi/2. We disprove this conjecture by a counterexample involving $$k = 6$$k=6 agents. We also show that the conjecture is true for $$k \le 3$$k≤3.

AB - Suppose we want to patrol a fence (line segment) using $$k$$k mobile agents with given speeds $$v _1$$v1,.., $$v _k$$vk 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 $$(v _1 + \cdots + v _k)/2$$(v1+⋯+vk)/2, which is achieved by the simple strategy where each agent $$i$$i moves back and forth in a segment of length $$v _i / 2$$vi/2. We disprove this conjecture by a counterexample involving $$k = 6$$k=6 agents. We also show that the conjecture is true for $$k \le 3$$k≤3.

UR - http://www.scopus.com/inward/record.url?scp=85027957380&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027957380&partnerID=8YFLogxK

U2 - 10.1007/s00446-014-0226-3

DO - 10.1007/s00446-014-0226-3

M3 - Article

VL - 28

SP - 147

EP - 154

JO - Distributed Computing

JF - Distributed Computing

SN - 0178-2770

IS - 2

ER -