  The problem of makespan optimal solving of cooperative path finding (CPF) is
addressed in this paper. The task in CPF is to relocate a group of agents in a
non-colliding way so that each agent eventually reaches its goal location from
the given initial location. The abstraction adopted in this work assumes that
agents are discrete items moving in an undirected graph by traversing edges.
Makespan optimal solving of CPF means to generate solutions that are as short
as possi-ble in terms of the total number of time steps required for the
execution of the solution.
  We show that reducing CPF to propositional satisfiability (SAT) represents a
viable option for obtaining makespan optimal solutions. Several encodings of
CPF into propositional formulae are suggested and experimentally evaluated. The
evaluation indicates that SAT based CPF solving outperforms other makespan
optimal methods significantly in highly constrained situations (environments
that are densely occupied by agents).
