# Fence patrolling by mobile agents with distinct speeds

Akitoshi Kawamura, Yusuke Kobayashi

21 引用 (Scopus)

### 抄録

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.

元の言語 英語 147-154 8 Distributed Computing 28 2 https://doi.org/10.1007/s00446-014-0226-3 出版済み - 1 1 2015

Fences
Mobile agents
Mobile Agent
Distinct
Disprove
Line segment
Counterexample
Unit

### All Science Journal Classification (ASJC) codes

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

### これを引用

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

：: Distributed Computing, 巻 28, 番号 2, 01.01.2015, p. 147-154.

Kawamura, Akitoshi ; Kobayashi, Yusuke. / Fence patrolling by mobile agents with distinct speeds. ：: Distributed Computing. 2015 ; 巻 28, 番号 2. pp. 147-154.
title = "Fence patrolling by mobile agents with distinct speeds",
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.",
author = "Akitoshi Kawamura and Yusuke Kobayashi",
year = "2015",
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doi = "10.1007/s00446-014-0226-3",
language = "English",
volume = "28",
pages = "147--154",
journal = "Distributed Computing",
issn = "0178-2770",
publisher = "Springer Verlag",
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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.

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U2 - 10.1007/s00446-014-0226-3

DO - 10.1007/s00446-014-0226-3

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JO - Distributed Computing

JF - Distributed Computing

SN - 0178-2770

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