A Theoretical Framework for Parallel Lifelong MAPF Using Group Decentralized Planning

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Lifelong Multi-Agent Path Finding (L-MAPF) — where agents continuously receive new destinations — is central to warehouse robotics, logistics, and drone fleets. Rolling-Horizon Collision Resolution (RHCR) is the leading framework for this, but its computational cost limits it to modest agent counts. This paper takes two steps. First, it theoretically proves RHCR is near-optimal in a discounted MDP formulation of L-MAPF — a formal guarantee that was previously assumed but not proven. Second, it introduces GD-RHCR (Group Decentralized RHCR), which partitions agents based on a transitive communication scheme and plans for each group in parallel. Crucially, the paper proves GD-RHCR achieves guarantees exponentially close to optimal — comparable to vanilla RHCR — establishing a theoretical duality between RHCR's time-based restrictions and GD-RHCR's space-based partitioning. In practice, GD-RHCR achieves high throughput that scales to larger agent counts while cutting per-plan cost significantly, across varying map types. For warehouse and logistics teams hitting RHCR scaling limits, this is a potentially drop-in improvement.