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A Quasi-Polynomial Algorithm for Well-Spaced Hyperbolic TSP

Author Sándor Kisfaludi-Bak

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Sándor Kisfaludi-Bak
  • Max Planck Institute for Informatics, Saarbrücken, Germany

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Sándor Kisfaludi-Bak. A Quasi-Polynomial Algorithm for Well-Spaced Hyperbolic TSP. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.SoCG.2020.55

Abstract

We study the traveling salesman problem in the hyperbolic plane of Gaussian curvature -1. Let α denote the minimum distance between any two input points. Using a new separator theorem and a new rerouting argument, we give an n^{O(log² n)max(1,1/α)} algorithm for Hyperbolic TSP. This is quasi-polynomial time if α is at least some absolute constant, and it grows to n^O(√n) as α decreases to log² n/√n. (For even smaller values of α, we can use a planarity-based algorithm of Hwang et al. (1993), which gives a running time of n^O(√n).)

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Computational geometry
  • Hyperbolic geometry
  • Traveling salesman

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