Network Decontamination with a Single Agent

Faults and viruses often spread in networked environments by propa10 gating from site to neighboring site. We model this process of network contamina11 tion by graphs. Consider a graph G = (V,E), whose vertex set is contaminated 12 and our goal is to decontaminate the set V (G) using mobile decontamination 13 agents that traverse along the edge set of G. Temporal immunity τ(G) ≥ 0 is 14 defined as the time that a decontaminated vertex of G can remain continuously 15 exposed to some contaminated neighbor without getting infected itself. The im16 munity number of G, ιk(G), is the least τ that is required to decontaminate G 17 using k agents. We study immunity number for some classes of graphs corre18 sponding to network topologies and present upper bounds on ι1(G), in some 19 cases with matching lower bounds. Variations of this problem have been exten20 sively studied in literature, but proposed algorithms have been restricted to mono21 tone strategies, where a vertex, once decontaminated, may not be recontaminated. 22 We exploit nonmonotonicity to give bounds which are strictly better than those 23 derived using monotone strategies. 24