Brief Announcement: Distributed Exclusive and Perpetual Tree Searching

We tackle a version of the well known graph searching problem where a team of robots aims at capturing an intruder in a graph. The robots and the intruder move between the graph nodes. The intruder is invisible, arbitrary fast, and omniscient. It is caught whenever it stands on a node occupied by a robot, and cannot escape to a neighboring node. We study graph searching in the CORDA model of mobile computing: robots are asynchronous and perform cycles of Look-Compute-Move actions. Moreover, motivated by physical constraints and similarly to some previous works, we assume the exclusivity property, stating that no two or more robots can occupy the same node at the same time. In addition, we assume that the network and the robots are anonymous. Finally, robots are oblivious, i.e., each robot performs its move actions based only on its current "vision" of the positions of the other robots. Our objective is to characterize, for a graph G, a set of integers such that for every integer k in the set, perpetual graph searching can be achieved by a team of k robots starting from any k distinct nodes in G. One of our main results is a full characterization of this set, for any asymmetric tree. Towards providing a characterization for all trees, including trees with non-trivial automorphisms, we have also provided a set of positive and negative results, including a full characterization for any line. All our positive results are based on the design of graph searching algorithms.