The GRAPH-CLEAR problem: definition, theoretical properties and its connections to multirobot aided surveillance

In this paper we present a novel graph theoretic problem, called GRAPH-CLEAR, useful to model surveillance tasks where multiple robots are used - to detect all possible intruders in a given indoor environment. We provide a formal definition of the problem and we investigate its basic theoretical properties, showing that the problem is NP-complete. We then present an algorithm to compute a strategy for the restriction of the problem to trees and present a method how to use this solution in applications. The method is then tested in simple simulations. GRAPH-CLEAR is useful to describe multirobot pursuit evasion games when robots have limited sensing capabilities, i.e. multiple agents are needed to perform basic patrolling operations.