Domain Design for the Cops and Robbers Problem

Abstract

Cops and Robbers is a well-studied problem in graph theory. The setting consists of a robber and one or more cops placed on an undirected graph. Taking turns moving throughout the graph, the cops try to capture the robber. The property of interest is whether $k$ cops suffice to ensure at least one cop occupies the same vertex as the robber, after a finite number of turns, given any configuration of their initial placement; if successful, the graph is referred to as ``$k$-copwin''. In this work, we cast the problem of determining whether a graph is $k$-copwin as a non-deterministic planning problem and use state-of-the-art planners to compute this property. The cop movement is cast as non-deterministic movement (to capture all possible strategies), while the robber movement is deterministic in nature. We also extend the base model using several variations from the graph theory literature.