A Polynomial Time Algorithm to Compute Geodesics in CAT(0) Cubical Complexes
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 (Adv. in Appl. Math, 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.
Geodesic
CAT(0) Space
Cubical Complex
Theory of computation~Computational geometry
78:1-78:14
Regular Paper
The work was supported by JSPS KAKENHI Grant Number 17K00029, and by JST ERATO Grant Number JPMJER1201, Japan.
https://arxiv.org/abs/1710.09932
Koyo
Hayashi
Koyo Hayashi
Department of Mathematical Informatics, University of Tokyo, Tokyo 113-8656, Japan
10.4230/LIPIcs.ICALP.2018.78
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Koyo Hayashi
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