Optimal Unlabeled Pebble Motion on Trees and its Application to Multi-Agent Path Finding
This provides an efficient solution for path planning in tree-structured environments, applicable to multi-agent systems, though it is incremental as it builds on existing pebble motion problems.
The paper tackled the Unlabeled Pebble Motion on Trees problem by developing the first optimal algorithm that runs in linear time relative to input and output sizes, and extended it to solve unlabeled Multi-Agent Path Finding in trees with new bounds on optimal makespan, sum of costs, and plan length.
Given a tree, a set of pebbles initially stationed at some nodes of the tree, and a set of target nodes, the Unlabeled Pebble Motion on Trees problem (UPMT) asks to find a plan to move the pebbles one-at-a-time from the starting nodes to the target nodes along the edges of the tree while minimizing the number of moves. This paper proposes the first optimal algorithm for UPMT that is asymptotically as fast as possible, as it runs in a time linear in the size of the input (the tree) and the size of the output (the optimal plan). We extend this to solve unlabeled Multi-Agent Path Finding (MAPF) in trees, providing novel bounds on optimal makespan, sum of costs, and pebble motion plan length.