Computing braid groups of graphs with applications to robot motion planning

V. Kurlin

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arXiv · 0908.1067

Computing braid groups of graphs with applications to robot motion planning

V. Kurlin

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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.

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V. Kurlin. 2009-08-07. Computing braid groups of graphs with applications to robot motion planning. https://arxiv.org/abs/0908.1067

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