Black Hole Search by Mobile Agents in Hypercubes and Related Networks

Mobile agents operating in networked environments face threats from other agents as well as from the hosts (i.e., network sites) they visit. A black hole is a harmful host that destroys incoming agents without leaving any trace. To determine the location of such a harmful host is a dangerous but crucial task, called black hole search. The most important parameter for a solution strategy is the number of agents it requires (the size); the other parameter of interest is the total number of moves performed by the agents (the cost). Any solution requires moves in general networks; the same lower bound holds for rings. In this paper we show that this lower bound does not hold for hypercubes and related networks. In fact, we present a general strategy which allows two agents to locate the black hole with moves in hypercubes, cube-connected cycles, star graphs, wrapped butterflies, chordal rings, as well as in multidimensional meshes and tori of restricted diameter.