A polynomial time algorithm to compute geodesics in CAT(0) cubical complexes

10/26/2017

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by   Koyo Hayashi, et al.

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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 (2011) as a subroutine. Our algorithm is applicable to any CAT(0) space in which geodesics between two close points can be computed, not limited to CAT(0) cubical complexes.