TY - JOUR

T1 - Fence patrolling by mobile agents with distinct speeds

AU - Kawamura, Akitoshi

AU - Kobayashi, Yusuke

N1 - Funding Information:
A preliminary version of this paper was presented at the 23rd International Symposium on Algorithms and Computation []. Supported in part by KAKENHI (Grant-in-Aid for Scientific Research, Japan).
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.

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

M3 - Article

AN - SCOPUS:85027957380

VL - 28

SP - 147

EP - 154

JO - Distributed Computing

JF - Distributed Computing

SN - 0178-2770

IS - 2

ER -