Computing braid groups of graphs with applications to robot motion planning

Kurlin, V.

Abstract

An algorithm is designed to write down presentations of graph braid groups. Generators are represented in terms of actual motions of robots moving without collisions on a given connected graph. A key ingredient is a new motion planning algorithm whose complexity is linear in the number of edges and is 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.

Citation

Kurlin, V. (2012). Computing braid groups of graphs with applications to robot motion planning. Homology, Homotopy and Applications, 14(1), 159-180. https://doi.org/10.4310/hha.2012.v14.n1.a8

• Journal Article Type: Article
• Publication Date: Jan 1, 2012
• Deposit Date: Oct 24, 2012
• Publicly Available Date: Apr 9, 2013
• Journal: Homology, Homotopy and Applications
• Print ISSN: 1532-0073
• Electronic ISSN: 1532-0081
• Publisher: International Press
• Peer Reviewed: Peer Reviewed
• Volume: 14
• Issue: 1
• Pages: 159-180
• DOI: https://doi.org/10.4310/hha.2012.v14.n1.a8
• Keywords: Graph, Braid group, Conguration space, Fundamental group, Homotopy type.
• Public URL: https://durham-repository.worktribe.com/output/1494707