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Fast algorithms for optimal multi-robot path planning are sought after in real-world applications. Known methods, however, generally do not simultaneously guar- antee good solution optimality and good (e.g., polynomial) running time. In this work, we develop a first low-polynomial running time algorithm, called SplitAndGroup (SaG), that solves the multi-robot path planning problem on grids and grid-like environments, and produces constant factor makespan optimal solutions on average over all problem in- stances. That is, SaG is an average case O(1)-approximation algorithm and computes solutions with sub-linear makespan. SaG is capable of handling cases when the density of robots is extremely high - in a graph-theoretic setting, the al- gorithm supports cases where all vertices of the underly- ing graph are occupied. SaG attains its desirable proper- ties through a careful combination of a novel divide-and- conquer technique, which we denote as global decoupling, and network flow based methods for routing the robots. Solutions from SaG, in a weaker sense, are also a constant factor approximation on total distance optimality.
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Expected 1.x Makespan-Optimal Multi-Agent Path Finding on Grid Graphs in Low Polynomial Time
Multi-Agent Path Finding (MAPF) is NP-hard to solve optimally, even on graphs, suggesting no polynomial-time algorithms can compute exact optimal solutions for them. This raises a natural question: How optimal can polynomial-time algorithms reach? Whereas algorithms for computing constant-factor optimal solutions have been developed, the constant factor is generally very large, limiting their application potential. In this work, among other breakthroughs, we propose the first low-polynomial-time MAPF algorithms delivering 1-1.5 (resp., 1-1.67) asymptotic makespan optimality guarantees for 2D (resp., 3D) grids for random instances at a very high 1/3 agent density, with high probability. Moreover, when regularly distributed obstacles are introduced, our methods experience no performance degradation. These methods generalize to support 100% agent density.Regardless of the dimensionality and density, our high-quality methods are enabled by a unique hierarchical integration of two key building blocks. At the higher level, we apply the labeled Grid Rearrangement Algorithm (GRA), capable of performing efficient reconfiguration on grids through row/column shuffles. At the lower level, we devise novel methods that efficiently simulate row/column shuffles returned by GRA. Our implementations of GRA-based algorithms are highly effective in extensive numerical evaluations, demonstrating excellent scalability compared to other SOTA methods. For example, in 3D settings, GRA-based algorithms readily scale to grids with over 370,000 vertices and over 120,000 agents and consistently achieve conservative makespan optimality approaching 1.5, as predicted by our theoretical analysis.
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- PAR ID:
- 10573391
- Publisher / Repository:
- JAIR
- Date Published:
- Journal Name:
- Journal of Artificial Intelligence Research
- Volume:
- 81
- ISSN:
- 1076-9757
- Page Range / eLocation ID:
- 443 to 479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Fast algorithms for optimal multi-robot path planning are sought after in both research and real-world applications. Known methods, however, generally do not simultaneously guarantee good solution optimality and fast run time for difficult instances. In this work, we develop a low-polynomial running time algorithm, called SplitAndGroup, that solves the multi-robot path planning problem on grids and grid-like environments, and produces constant factor time- and distance-optimal solutions, in expectation. In particular, SplitAndGroup computes solutions with sub-linear makespan. SplitAndGroup is capable of handling cases when the density of robot is extremely high - in a graph-theoretic setting, the algorithm supports cases where all vertices of the underlying graph are occupied by robots. SplitAndGroup attains its desirable properties through a careful combination of divide-and-conquer technique and network flow based methods for routing the robots.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1613/jair.1.16299
