Discrete and Computational Geometry | 2019
A Polynomial Time Algorithm to Compute Geodesics in CAT(0) Cubical Complexes
Abstract
This paper presents the first polynomial time algorithm to compute geodesics in a CAT(0) cubical complex in general dimension. The algorithm is a simple iterative method to update breakpoints of a path joining two points using Owen and Provan’s algorithm (IEEE/ACM Trans Comput Biol Bioinform 8(1):2–13, 2011) as a subroutine. Our algorithm is applicable to any path in any CAT(0) space in which geodesics between two close points can be computed, not limited to CAT(0) cubical complexes.