Lower Bounds for the Capture Time: Linear, Quadratic, and Beyond
Abstract
In the classical game of Cops and Robbers on graphs, the capture time is defined by the least number of moves needed to catch all robbers with the smallest amount of cops that suffice. While the case of one cop and one robber is well understood, it is an open question how long it takes for multiple cops to catch multiple robbers. We show that capturing ℓ∈O(n) robbers can take Ω(ℓ⋅n) time, inducing a capture time of up to Ω(n2) . For the case of one cop, our results are asymptotically optimal. Furthermore, we consider the case of a superlinear amount of robbers, where we show a capture time of Ω(n2⋅log(ℓ/n)) .
Top- Foerster, Klaus-Tycho
- Nuridini, Rijad
- Uitto, Jara
- Wattenhofer, Roger
Supplemental Material
Shortfacts
Category |
Paper in Conference Proceedings or in Workshop Proceedings (Paper) |
Event Title |
22nd International Colloquium on Structural Information and Communication Complexity (SIROCCO 2015) |
Divisions |
Communication Technologies |
Subjects |
Theoretische Informatik |
Event Location |
Montserrat, Spain |
Event Type |
Conference |
Event Dates |
15-17 Jul 2015 |
Date |
July 2015 |
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