A Polynomial Time Algorithm to Compute Geodesics in CAT(0) Cubical Complexes

Author Koyo Hayashi

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Koyo Hayashi
  • Department of Mathematical Informatics, University of Tokyo, Tokyo 113-8656, Japan

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Koyo Hayashi. A Polynomial Time Algorithm to Compute Geodesics in CAT(0) Cubical Complexes. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 78:1-78:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Geodesic
  • CAT(0) Space
  • Cubical Complex


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