Decontaminating Chordal Rings and Tori Using Mobile Agents

In this paper we consider a network where an intruder is moving “contaminating” the nodes it passes by, and we focus on the problem of decontaminating such a network by a team of mobile agents. The contamination/decontamination process has the following asynchronous dynamics: when the team is deployed all nodes are assumed to be contaminated, when an agent transits on a node, it will clean the node, when the node is left with no agent, the node will be recontaminated as soon as at least one of its neighbours is contaminated. We study the problem in asynchronous chordal ring networks and in tori. We consider two variations of the model: one where agents have only local knowledge, the other in which they have “visibility”, i.e., they can “see” the state of their neighbouring nodes. We first derive lower bounds on the minimum number of agents necessary for the decontamination. In the case of chordal rings we show that the number of agents necessary to perform the cleaning does not depend on the size of the network; in fact it is linear in the length of the longest chord (provided that it is not too long). In the case of a torus, the minimum number of agents is equal to 2 · h, where h is the smallest dimension. We then propose optimal strategies for decontamination and 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. School of Information Technology and Engineering, University of Ottawa, 800 King Edward, Ottawa, Canada. {mhuang,flocchin}@site.uottawa.ca. Dip. di Matematica e Informatica, 34100, Trieste, Italy. [email protected]