A Self-stabilizing Algorithm for Graph Searching in Trees
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Network decontamination with temporal immunity by cellular automata
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
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Consider a tree network that has been contaminated by apersistent and active virus: when infected, a network sitewill continuously attempt to spread the virus to all itsneighbours. The decontamination problem is that ofdisinfecting the entire network using a team of mobile antiviralsystem agents, called cleaners, avoiding anyrecontamination of decontaminated areas. A cleaner is able todecontaminate any infected node it visits; once the cleanerdeparts, the decontaminated node is immune for t ≥ 0time units to viral attacks from infected neighbours. After theimmunity time t is elapsed, re-contamination canoccur. The primary research objective is to determine the minimumteam size, as well as the solution strategy, thatis the protocol that would enable such a minimal team of cleanersto perform the task. The network decontamination problem has beenextensively investigated in the literature, and a very large numberof studies exist on the subject. However, all the existing work islimited to the special case t = 0. In this paper weexamine the tree decontamination problem for any value t≥ 0. We determine the minimum team size necessary to disinfectany given tree with immunity time t. Further we show howto compute for all nodes of the tree the minimum team size andimplicitly the solution strategy starting from each starting node;these computations use a total of θ(n) time(serially) or θ(n) messages(distributively). We then provide a complete structuralcharacterization of the class of trees that can be decontaminatedwith k agents and immunity time t; we do so byidentifying the forbidden subgraphs and analyzing theirproperties. Finally, we consider generic decontaminationalgorithms, i.e. protocols that work unchanged in a large class oftrees, with little knowledge of their topological structure. Weprove that, for each immunity time t ≥ 0, all trees ofheight at most h can be decontaminated by a team of$k=\lfloor {{2 h} \over t+2 }\rfloor$ agents whose only knowledgeof the tree is the bound h. The proof is constructive.