Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Fence patrolling by mobile agents with distinct speeds

Fence patrolling by mobile agents with distinct speeds Suppose we want to patrol a fence (line segment) using $$k$$ k mobile agents with given speeds $$v _1$$ v 1 , ..., $$v _k$$ 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 $$(v _1 + \cdots + v _k)/2$$ ( v 1 + ⋯ + v k ) / 2 , which is achieved by the simple strategy where each agent  $$i$$ i moves back and forth in a segment of length $$v _i / 2$$ v i / 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 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Distributed Computing Springer Journals

Fence patrolling by mobile agents with distinct speeds

Distributed Computing , Volume 28 (2) – Aug 20, 2014

Loading next page...
 
/lp/springer-journals/fence-patrolling-by-mobile-agents-with-distinct-speeds-UWB52Aehp9

References (1)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Computer Science; Computer Communication Networks; Computer Hardware; Computer Systems Organization and Communication Networks; Software Engineering/Programming and Operating Systems; Theory of Computation
ISSN
0178-2770
eISSN
1432-0452
DOI
10.1007/s00446-014-0226-3
Publisher site
See Article on Publisher Site

Abstract

Suppose we want to patrol a fence (line segment) using $$k$$ k mobile agents with given speeds $$v _1$$ v 1 , ..., $$v _k$$ 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 $$(v _1 + \cdots + v _k)/2$$ ( v 1 + ⋯ + v k ) / 2 , which is achieved by the simple strategy where each agent  $$i$$ i moves back and forth in a segment of length $$v _i / 2$$ v i / 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 .

Journal

Distributed ComputingSpringer Journals

Published: Aug 20, 2014

There are no references for this article.