We consider an Anonymous Multi-Agent Path-Finding (AMAPF) problem where the set of agents is confined to a graph, a set of goal vertices is given and each of these vertices has to be reached by some agent. The problem is to find an assignment of the goals to the agents as well as the collision-free paths, and we are interested in finding the solution with the optimal makespan. A well-established approach to solve this problem is to reduce it to a special type of a graph search problem, i.e. to the problem of finding a maximum flow on an auxiliary graph induced by the input one. The size of the former graph may be very large and the search on it may become a bottleneck. To this end, we suggest a specific search algorithm that leverages the idea of exploring the search space not through considering separate search states but rather bulks of them simultaneously. That is, we implicitly compress, store and expand bulks of the search states as single states, which results in high reduction in runtime and memory. Empirically, the resultant AMAPF solver demonstrates superior performance compared to the state-of-the-art competitor and is able to solve all publicly available MAPF instances from the well-known MovingAI benchmark in less than 30 seconds.

Safe Interval Path Planning (SIPP) is a powerful algorithm for solving a single-agent pathfinding problem where the agent is confined to a graph and certain vertices/edges of this graph are blocked at certain time intervals due to dynamic obstacles that populate the environment. The original SIPP algorithm relies on the assumption that the agent is able to stop instantaneously. However, this assumption often does not hold in practice, e.g. a mobile robot moving at a cruising speed cannot stop immediately but rather requires gradual deceleration to a full stop that takes time. In other words, the robot is subject to kinodynamic constraints. Unfortunately, as we show in this work, in such a case, the original SIPP is incomplete. To this end, we introduce a novel variant of SIPP that is provably complete and optimal for planning with acceleration/deceleration. In the experimental evaluation, we show that the key property of the original SIPP still holds for the modified version: it performs much fewer expansions compared to A* and, as a result, is notably faster.