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COMGEO
2011
ACM

Improved bounds for cops-and-robber pursuit

8 years 1 months ago
Improved bounds for cops-and-robber pursuit
We prove that n cops can capture (that is, some cop can get less than unit distance from) a robber in a continuous square region with side length less than √ 5n and hence that n/ √ 5 +1 cops can capture a robber in a square with side length n. We extend these results to three dimensions, proving that 0.34869 · · ·n2 + O(n) cops can capture a robber in a n × n × n cube and that a robber can forever evade fewer than 0.02168 · · ·n2 + O(n) cops in that cube. Key words. Pursuit, evasion, cops and robber, lion and man, rabbit and robot AMS(MOS) subject classifications. 49N75 Under what conditions can a robber evade cops on fixed patrol routes (that is, the cops move non-adaptively, independent of the robber’s movements)? Pursuit problems have been studied for centuries, with recent results prompted by Dumitrescu, Suzuki, and Zylinski [6] who asked, among other questions, what is the maximum number of cops that a robber can evade, that is, stay at least unit distance away fro...
Laurent Alonso, Edward M. Reingold
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where COMGEO
Authors Laurent Alonso, Edward M. Reingold
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