Power-Aware Collective Tree Exploration

An n-node tree has to be explored by a group of k mobile robots deployed initially at the root. Robots traverse the edges of the tree until all nodes are visited. We would like to minimize maximal distance traveled by each robot (e.g. to preserve the battery power). First, we assume that a tree is known in advance. For this NP-hard problem we present a 2-approximation. Moreover, we present an optimal algorithm for a case where k is constant. From the 2-approximation algorithm we develop a fast 8-competitive online algorithm, which does not require a previous knowledge of the tree and collects information during the exploration. Furthermore, our online algorithm is distributed and uses only a local communication. We show a lower bound of 1.5 for the competitive ratio of any deterministic online algorithm.