Cops and robbers in graphs with large girth and Cayley graphs
Discrete Applied Mathematics
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
A game of cops and robbers played on products of graphs
Discrete Mathematics
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Chasing robbers on random graphs: Zigzag theorem
Random Structures & Algorithms
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The cops and robber game has been extensively studied under the assumption of optimal play by both the cops and the robber. In this paper we study the problem in which cops are chasing a drunk robber (that is, a robber who performs a random walk) on a graph. Our main goal is to characterize the ''cost of drunkenness''. Specifically, we study the ratio of expected capture times for the optimal version and the drunk robber one. We also examine the algorithmic side of the problem; that is, how to compute near-optimal search schedules for the cops. Finally, we present a preliminary investigation of the invisible robber game and point out differences between this game and graph search.