LIPIcs.SoCG.2024.81.pdf
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Faster Approximation Scheme for Euclidean k-TSP
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40th International Symposium on Computational Geometry (SoCG 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-06-06
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Acknowledgements
We thank Tobias Mömke, Noé Weeks, and Antoine Stark for discussions.
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Ernest van Wijland and Hang Zhou. Faster Approximation Scheme for Euclidean k-TSP. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 81:1-81:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SoCG.2024.81
Abstract
In the Euclidean k-traveling salesman problem (k-TSP), we are given n points in the d-dimensional Euclidean space, for some fixed constant d ≥ 2, and a positive integer k. The goal is to find a shortest tour visiting at least k points.
We give an approximation scheme for the Euclidean k-TSP in time n⋅2^O(1/ε^{d-1})⋅(log n)^{2d²⋅2^d}. This improves Arora’s approximation scheme of running time n⋅k⋅(log n)^(O(√d/ε))^{d-1}} [J. ACM 1998]. Our algorithm is Gap-ETH tight and can be derandomized by increasing the running time by a factor O(n^d).
Subject Classification
ACM Subject Classification
- Mathematics of computing → Combinatorial optimization
Keywords
- approximation algorithms
- optimization
- traveling salesman problem
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References
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