An algorithm with improved complexity for pebble motion/multi-agent path finding on trees
Multiagent Systems
2024-04-10 v1
Abstract
The pebble motion on trees (PMT) problem consists in finding a feasible sequence of moves that repositions a set of pebbles to assigned target vertices. This problem has been widely studied because, in many cases, the more general Multi-Agent path finding (MAPF) problem on graphs can be reduced to PMT. We propose a simple and easy to implement procedure, which finds solutions of length O(knc + n^2), where n is the number of nodes, is the number of pebbles, and c the maximum length of corridors in the tree. This complexity result is more detailed than the current best known result O(n^3), which is equal to our result in the worst case, but does not capture the dependency on c and k.
Cite
@article{arxiv.2307.12770,
title = {An algorithm with improved complexity for pebble motion/multi-agent path finding on trees},
author = {Stefano Ardizzoni and Irene Saccani and Luca Consolini and Marco Locatelli and Bernhard Nebel},
journal= {arXiv preprint arXiv:2307.12770},
year = {2024}
}