Bounding an Optimal Search Path with a Game of Cop and Robber on Graphs

Abstract

Abstract. In search theory, the goal of the Optimal Search Path (OSP) problem is to find a finite length path maximizing the probability that a searcher detects a lost wanderer on a graph. We propose to bound the probability of finding the wanderer in the remaining search time by relaxing the problem into a stochastic game of cop and robber from graph theory. We discuss the validity of this bound and demonstrate its effectiveness on a constraint programming model of the problem. Experimental results show how our novel bound compares favorably to the DMEAN bound from the literature, a state-of-the-art bound based on a relaxation of the OSP into a longest path problem.

The one-cop-moves game on planar graphs

“…The cops and robbers game has attracted considerable attention from the graph theory community, owing in part to its connections to various graph parameters, as well as the large number of interesting combinatorial problems arising from the study of the cop number. In addition, due to the relative simplicity and naturalness of the cops and robbers game, it has served as a model for studying problems in areas of applied computer science such as artificial intelligence, robotics and the theory of optimal search [8,11,15,21]. This paper examines a variant of the cops and robbers game, known alternately as the oneactive-cop game [17], lazy cops and robbers game [3,4,22] or the one-cop-moves game [25].…”