Divide and Collapse: MAPF-Collapse via Exact Decomposition into Independent Sub-Instances

Oren Salzman

In this work we study the problem of MAPFC, a post-optimization step for Multi-Agent Path Finding (MAPF) plans where we are given a feasible plan produced by a modern MAPF solver and are tasked with removing avoidable moves while preserving feasibility. This NP-hard problem naturally arises when using learning-based state-of-the-art (SOTA) solvers which construct plans that contain redundant moves that can be removed. Recently, Tang et al. presented Judgelight, which uses Integer Linear Programming (ILP) to solve MAPFC. Importantly, the ILP is constructed over all agents jointly, so its cost is governed by the full instance rather than by the small coupled residue that actually requires joint reasoning. Our key insight, motivating this work, is that MAPFC instances naturally decompose into independent sub-problems, most of which involve a single agent and can be solved without any inter-agent reasoning. To this end, we first identify which agents need to coordinate their motion and partition the instance into sub-problems accordingly. For the cases where no coordination is required, we introduce an extremely lightweight solver that is $\approx\!1{,}900\times$ faster than…