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A (5/3+ε)-Approximation for Tricolored Non-Crossing Euclidean TSP

Authors Júlia Baligács , Yann Disser , Andreas Emil Feldmann , Anna Zych-Pawlewicz

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Author Details

Júlia Baligács
  • Technische Universität Darmstadt, Germany
Yann Disser
  • Technische Universität Darmstadt, Germany
Andreas Emil Feldmann
  • University of Sheffield, UK
Anna Zych-Pawlewicz
  • University of Warsaw, Poland

Funding

  • Zych-Pawlewicz, Anna: This work is a part of project BOBR that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 948057).

Cite AsGet BibTex

Júlia Baligács, Yann Disser, Andreas Emil Feldmann, and Anna Zych-Pawlewicz. A (5/3+ε)-Approximation for Tricolored Non-Crossing Euclidean TSP. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.15

Abstract

In the Tricolored Euclidean Traveling Salesperson problem, we are given k = 3 sets of points in the plane and are looking for disjoint tours, each covering one of the sets. Arora (1998) famously gave a PTAS based on "patching" for the case k = 1 and, recently, Dross et al. (2023) generalized this result to k = 2. Our contribution is a (5/3+ε)-approximation algorithm for k = 3 that further generalizes Arora’s approach. It is believed that patching is generally no longer possible for more than two tours. We circumvent this issue by either applying a conditional patching scheme for three tours or using an alternative approach based on a weighted solution for k = 2.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Mathematics of computing → Approximation algorithms
  • Theory of computation → Computational geometry
Keywords
  • Approximation Algorithms
  • geometric Network Optimization
  • Euclidean TSP
  • non-crossing Structures

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