Decontamination of chordal rings and tori

In this paper, we consider the problem of decontaminating a network, i.e., protecting it from unwanted and dangerous intrusions. Initially all nodes are contaminated and a team of agents is deployed to clean the entire network. When an agent transits on a node, it can clean it, when the node is left unguarded, however, it will be recontaminated as soon as at least one of its neighbour is contaminated. We study the problem in asynchronous chordal ring networks with n nodes and chord lengths d₁ = 1, d₂, ..., d_k, and in tori. We consider two variations of the model: one where an agent has only local knowledge, the other in which it has "visibility", i.e., it can "see" the state of its neighbouring nodes. We first show that, when the largest chord d_k is not too large (d_k les radicn), the number of agents necessary to perform the task in chordal rings does not depend on the size of the network but only on the length of the longest chord. We also show a lower bound on the number of agents for the torus topology. We then propose tight strategies for decontamination. We analyse the number of moves and the time complexity of the decontamination algorithms showing that the visibility assumption allows us to decrease substantially both complexity measures. Another advantage of the "visibility model" is that agents move independently and autonomously without requiring any coordination