Collision-free network exploration

Mobile agents start at different nodes of an n-node network. The agents synchronously move along the network edges in a collision-free way, i.e., in no round two agents may occupy the same node. An agent has no knowledge of the number and initial positions of other agents. We are looking for the shortest time required to reach a configuration in which each agent has visited all nodes and returned to its starting location. In the scenario when each mobile agent knows the map of the network, we provide tight (up to a constant factor) lower and upper bounds on the collision-free exploration time in arbitrary graphs, and the exact bound for the trees. In the second scenario, where the network is unknown to the agents, we propose collision-free exploration strategies running in O(n²) rounds in tree networks and in O(n⁵log⁡n) rounds in networks with an arbitrary topology.