Computing braid groups of graphs with applications to robot motion planning

Details Computing braid groups of graphs with applications to robot motion planning Computing braid groups of graphs with applications to robot motion planning

2009-08-07

arxiv.org/abs/0908.1067v1

Mathematics

Geometric Topology

16 pages, 10 figures

Scientific paper

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.

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