Maximal Exploration of Trees with Energy-Constrained Agents.

We wish to explore an unknown tree with a team of k u003e= 1 initially collocated mobile agents. Each agent has limited energy and cannot,as a result, traverse more than B edges. The goal is to maximize the number of nodes collectively visited by all agents during the execution.Initially, the agents have no knowledge about the structure of the tree,but they gradually discover the topology as they traverse new edges. We assume that the agents can communicate with each other at arbitrary distances, therefore the knowledge obtained by one agent after traversing an edge is instantaneously transmitted to the other agents.We propose an intuitive algorithm based on depth-first search and westudy its performance compared to the optimal solution that we could obtain if we knew in advance the map of the tree. We prove that this algorithm has a constant competitive ratio. We also provide a lower bound on the competitive ratio of any algorithm.