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arXiv · 1710.09932

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

Koyo Hayashi
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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 Miller, Owen and Provan's algorithm (2015) 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.

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Koyo Hayashi. 2017-10-26. A polynomial time algorithm to compute geodesics in CAT(0) cubical complexes. https://arxiv.org/abs/1710.09932

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