Rendezvous of mobile agents in unknown graphs with faulty links

Abstract

A group of identical mobile agents moving asynchronously among the nodes of an anonymous network have to gather together in a single node of the graph. This problem known as the (asynchronous anonymous multi-agent) rendezvous problem has been studied extensively but only for networks that are safe or fault-free. In this paper, we consider the case when some of the edges in the network are dangerous or faulty such that any agent travelling along one of these edges would be destroyed. The objective is to minimize the number of agents that are destroyed and achieve rendezvous of all the surviving agents. We determine under what conditions this is possible and present algorithms for achieving rendezvous in such cases. Our algorithms are for arbitrary networks with an arbitrary number of dangerous channels; thus our model is a generalization of the case where all the dangerous channels lead to single node, called the Black Hole. We do not assume prior knowledge of the network topology; In fact, we show that knowledge of only a "tight" bound on the network size is sufficient for solving the problem, whenever it is solvable. © Springer-Verlag Berlin Heidelberg 2007.