Computing braid groups of graphs with applications to robot motion planning
Geometric Topology
2009-08-10 v1 Algebraic Topology
Abstract
We design an algorithm writing down presentations of graph braid groups. Generators are represented in terms of actual motions of robots moving without collisions on a given graph. A key ingredient is a new motion planning algorithm whose complexity is linear in the number of edges and quadratic in the number of robots. The computing algorithm implies that 2-point braid groups of all light planar graphs have presentations where all relators are commutators.
Cite
@article{arxiv.0908.1067,
title = {Computing braid groups of graphs with applications to robot motion planning},
author = {V. Kurlin},
journal= {arXiv preprint arXiv:0908.1067},
year = {2009}
}
Comments
16 pages, 10 figures