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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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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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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.

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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

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).

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