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Fast algorithms for optimal multi-robot path planning are sought after inreal-world applications. Known methods, however, generally do notsimultaneously guarantee good solution optimality and good (e.g., polynomial)running time. In this work, we develop a first low-polynomial running timealgorithm, called SplitAngGroup (SaG), that solves the multi-robot pathplanning problem on grids and grid-like environments, and produces constantfactor makespan optimal solutions on average over all problem instances. Thatis, SaG is an average case O(1)-approximation algorithm and computes solutionswith sub-linear makespan. SaG is capable of handling cases when the density ofrobots is extremely high - in a graph-theoretic setting, the algorithm supportscases where all vertices of the underlying graph are occupied. SaG attains itsdesirable properties through a careful combination of a noveldivide-and-conquer technique, which we denote as global decoupling, and networkflow based methods for routing the robots. Solutions from SaG, in a weakersense, are also a constant factor approximation on total distance optimality.

Average Case Constant Factor Time and Distance Optimal Multi-Robot Path Planning in Well-Connected Environments