Adversarial Cooperative Path-Finding: Complexity and Algorithms

The paper addresses a problem of adversarial cooperative path-finding (ACPF) which extends the well-studied problem of cooperative path-finding (CPF) with adversaries. In addition to cooperative path-finding where non-colliding paths for multiple agents connecting their initial positions and destinations are searched, consideration of agents controlled by the adversary is included in ACPF. This work is focused on both theoretical properties and practical solving techniques of the considered problem. We study computational complexity of the problem where we show that it is PSPACE-hard and belongs to the EXPTIME complexity class. Possible methods suitable for practical solving of the problem are introduced and thoroughly evaluated. Suggested solving approaches include greedy algorithms, minimax methods, Monte Carlo Tree Search, and adaptation of an algorithm for the cooperative version of the problem. Solving methods for ACPF were compared in a tournament in which all the pairs of suggested strategies were compared. Surprisingly frequent success rate of greedy methods and rather weaker results of Monte Carlo Tree Search were indicated by the conducted experimental evaluation.