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arXiv · 2402.13938

A $(5/3+{\epsilon})$-Approximation for Tricolored Non-crossing Euclidean TSP

Júlia Baligács·Yann Disser·Andreas Emil Feldmann·Anna Zych-Pawlewicz
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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 $(5/3+\epsilon)$-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, Anna Zych-Pawlewicz. 2024-02-21. A $(5/3+{\epsilon})$-Approximation for Tricolored Non-crossing Euclidean TSP. https://arxiv.org/abs/2402.13938

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