Domain Design for the Cops and Robbers Problem

Connor Little, Christian Muise

Abstract: The cops and robbers problem is a well-researched problem in graph theory. The problem consists of a robber and one or more cops placed on a graph. Taking turns moving throughout the graph, the cops try to capture the robbers. We model a non-deterministic version of this problem using automated planning. We then extend it using numerous variations within the literature. These variations include the variable speed robber and the friendly robber. Given a class of graphs, we can exhaustively generate domain-problem pairs for all problems and use these pairs to test the properties of the class – a systemic and exhaustive compilation of all planning models for a class of graphs through an automatic translation. Our work demonstrates planning is capable of solving the cops and robbers problem efficiently.