Integer programming models and algorithms for the graph decontamination problem with mobile agents

This paper considers the problem of using synchronous mobile agents to decontaminate the nodes of a graph given a spreading contamination. We begin by considering the problem of minimizing cleaning time, given initial agent and contamination locations. Then, we take as input a set of all possible locations in which a contamination can start, and examine problems in which we strategically pre-position agents. In one problem, we minimize the number of agents, and prescribe their initial locations, so that the graph can be cleaned within a time limit for any potential initial contamination. We also determine the best initial locations for some pre-determined number of agents to minimize expected cleaning time, given probability estimates of potential initial contamination locations. We analyze the complexity of each variant, and formulate the problems as mixed-integer programs. As an alternative method, we also provide a construction heuristic for the cleaning problem, and cutting-plane algorithms for the agent location problems. Computational results using these approaches demonstrate the efficacy of our procedures.