Multi-agent Pathfinding is a relevant problem in a wide range of domains, for example in robotics and video games research. Formally, the problem considers a graph consisting of vertices and edges, and a set of agents occupying vertices. An agent can only move to an unoccupied, neighbouring vertex, and the problem of finding the minimal sequence of moves to transfer each agent from its start location to its destination is an NP-hard problem. We present Push and Rotate, a new algorithm that is complete for Multi-agent Pathfinding problems in which there are at least two empty vertices. Push and Rotate first divides the graph into subgraphs within which it is possible for agents to reach any position of the subgraph, and then uses the simple push, swap, and rotate operations to find a solution; a post-processing algorithm is also presented that eliminates redundant moves. Push and Rotate can be seen as extending Luna and Bekris's Push and Swap algorithm, which we showed to be incomplete in a previous publication. In our experiments we compare our approach with the Push and Swap, MAPP, and Bibox algorithms. The latter algorithm is restricted to a smaller class of instances as it requires biconnected graphs, but can nevertheless be considered state of the art due to its strong performance. Our experiments show that Push and Swap suffers from incompleteness, MAPP is generally not competitive with Push and Rotate, and Bibox is better than Push and Rotate on randomly generated biconnected instances, while Push and Rotate performs better on grids.

Abstract. In context-aware route planning, there is a set of transportation agents each with a start and destination location on a shared infrastructure. Each agent wants to find a shortest-time route plan without colliding with any of the other agents, or ending up in a deadlock situation. We present a single-agent route planning algorithm that is both optimal and conflict-free. We also present a set of experiments that compare our algorithm to finding a conflict-free schedule along a fixed path. In particular, we will compare our algorithm to the approach where the shortest conflict-free schedule is chosen along one of k shortest paths. Although neither approach can guarantee optimality with regard to the total set of agent route plans -and indeed examples can be constructed to show that either approach can outperform the other -our experiments show that our approach consistently outperforms fixed-path scheduling.

We consider planning problems where a number of non-cooperative agents have to work on a joint problem. Such problems consist in completing a set of interdependent, hierarchically ordered tasks. Each agent is assigned a subset of tasks to perform for which it has to construct a plan. Since the agents are non-cooperative, they insist on planning independently and do not want to revise their individual plans when the joint plan has to be assembled from the individual plans. We present a general formal framework to study some computational aspects of this non-cooperative coordination problem and we establish some complexity results to identify some of the factors that contribute to the complexity of this problem. Finally, we illustrate our approach with an application to coordination in multi-modal logistic planning.

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Abstract. In multi-agent planning problems agents are requested to jointly solve a complex task consisting of a set of interrelated tasks. Since none of the agents is capable to solve the whole task on its own, usually each of them is assigned to a subset of tasks. If agents are dependent upon each other via interrelated tasks they are assigned to, moderately-coupled teams of agents are called for. Such teams solve the task by coordinating during or after planning and revising their plans if necessary. In this paper we show that such complex tasks also can be solved by looselycoupled teams of agents that are able to plan independently, although the computational complexity of the coordination problems involved is high. We also investigate some of the factors influencing this complexity.