  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.
