On the Complexity of Decontaminating an Hexagonal Mesh Network

We consider the problem of decontaminating a network infected by mobile viruses. The goal is to perform the task using as small a team of antiviral agents as possible, avoiding any recontamination of decontaminated areas; other cost measures include the amount of agents\´ movements across the network and the time required by the decontamination process. The network we consider is a regular cellular space, namely an Hexagonal Mesh. We examine the decontamination problem of such a network in two different settings, depending on the sensorial capabilities of the agents. In the first setting, the only knowledge that an agent has is local to the node in which it is currently residing; in the other setting, each agent can also "see " the state of the neighbouring nodes. We examine the complexity of decontamination in both settings; for each, we design strategies that are optimal in terms of number of agents employed and efficient in the other two cost measures. We show that visibility power allows a drastic decrease in time complexity, extending the known results for regular meshes.