3 Search Results for "Zhong, Xianghui"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.73
Counting Locally Optimal Tours in the TSP

Authors: Bodo Manthey and Jesse van Rhijn

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We show that the problem of counting 2-optimal tours in instances of the Travelling Salesperson Problem (TSP) on complete graphs is #P-complete. In addition, we show that the expected number of 2-optimal tours in random instances of the TSP on complete graphs is O(1.2098ⁿ √{n!}). Based on numerical experiments, we conjecture that the true bound is at most O(√{n!}), which is approximately the square root of the total number of tours.
Cite as

Bodo Manthey and Jesse van Rhijn. Counting Locally Optimal Tours in the TSP. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 73:1-73:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{manthey_et_al:LIPIcs.MFCS.2025.73,
  author =	{Manthey, Bodo and van Rhijn, Jesse},
  title =	{{Counting Locally Optimal Tours in the TSP}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{73:1--73:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.73},
  URN =		{urn:nbn:de:0030-drops-241807},
  doi =		{10.4230/LIPIcs.MFCS.2025.73},
  annote =	{Keywords: Travelling salesman problem, probabilistic analysis, local search, heuristics, 2-opt}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.9
Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model

Authors: Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the (1,2)-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on the closely related Maximum Path Cover Problem, which aims to find a collection of vertex-disjoint paths that covers the maximum number of edges in a graph. We propose an algorithm that, for any ε > 0, achieves a (2/3-ε)-approximation of the maximum path cover size for an n-vertex graph, using poly(1/ε) passes. This result improves upon the previous 1/2-approximation by Behnezhad et al. [Soheil Behnezhad et al., 2023] in the semi-streaming model. Building on this result, we design a semi-streaming algorithm that constructs a tour for an instance of (1,2)-TSP with an approximation factor of (4/3 + ε), improving upon the previous 3/2-approximation factor algorithm by Behnezhad et al. [Soheil Behnezhad et al., 2023]. Furthermore, we extend our approach to develop an approximation algorithm for the Maximum TSP (Max-TSP), where the goal is to find a Hamiltonian cycle with the maximum possible weight in a given weighted graph G. Our algorithm provides a (7/12 - ε)-approximation for Max-TSP in poly(1/(ε)) passes, improving on the previously known (1/2-ε)-approximation obtained via maximum weight matching in the semi-streaming model.
Cite as

Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke. Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{alipour_et_al:LIPIcs.STACS.2025.9,
  author =	{Alipour, Sharareh and Farokhnejad, Ermiya and M\"{o}mke, Tobias},
  title =	{{Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.9},
  URN =		{urn:nbn:de:0030-drops-228342},
  doi =		{10.4230/LIPIcs.STACS.2025.9},
  annote =	{Keywords: (1,2)-TSP, Max-TSP, Maximum Path Cover, Semi-Streaming Algorithms, Approximation Algorithms, Graph Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.83
On the Approximation Ratio of the k-Opt and Lin-Kernighan Algorithm for Metric and Graph TSP

Authors: Xianghui Zhong

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
The k-Opt and Lin-Kernighan algorithm are two of the most important local search approaches for the Metric TSP. Both start with an arbitrary tour and make local improvements in each step to get a shorter tour. We show that for any fixed k ≥ 3 the approximation ratio of the k-Opt algorithm for Metric TSP is O(√[k]{n}). Assuming the Erdős girth conjecture, we prove a matching lower bound of Ω(√[k]{n}). Unconditionally, we obtain matching bounds for k = 3,4,6 and a lower bound of Ω(n^{2/(3k-3)}). Our most general bounds depend on the values of a function from extremal graph theory and are tight up to a factor logarithmic in the number of vertices unconditionally. Moreover, all the upper bounds also apply to a parameterized version of the Lin-Kernighan algorithm with appropriate parameter. We also show that the approximation ratio of k-Opt for Graph TSP is Ω(log(n)/(log log(n))) and O({log(n)/(log log(n))}^{log₂(9)+ε}) for all ε > 0.
Cite as

Xianghui Zhong. On the Approximation Ratio of the k-Opt and Lin-Kernighan Algorithm for Metric and Graph TSP. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 83:1-83:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{zhong:LIPIcs.ESA.2020.83,
  author =	{Zhong, Xianghui},
  title =	{{On the Approximation Ratio of the k-Opt and Lin-Kernighan Algorithm for Metric and Graph TSP}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{83:1--83:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.83},
  URN =		{urn:nbn:de:0030-drops-129497},
  doi =		{10.4230/LIPIcs.ESA.2020.83},
  annote =	{Keywords: traveling salesman problem, metric TSP, graph TSP, k-Opt algorithm, Lin-Kernighan algorithm, approximation algorithm, approximation ratio.}
}
  • Refine by Type
  • 3 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 2 2025
  • 1 2020

  • Refine by Author
  • 1 Alipour, Sharareh
  • 1 Farokhnejad, Ermiya
  • 1 Manthey, Bodo
  • 1 Mömke, Tobias
  • 1 Zhong, Xianghui
  • Show More...

  • Refine by Series/Journal
  • 3 LIPIcs

  • Refine by Classification
  • 3 Theory of computation → Approximation algorithms analysis
  • 1 Theory of computation → Discrete optimization
  • 1 Theory of computation → Graph algorithms analysis
  • 1 Theory of computation → Randomness, geometry and discrete structures
  • 1 Theory of computation → Streaming, sublinear and near linear time algorithms

  • Refine by Keyword
  • 1 (1,2)-TSP
  • 1 2-opt
  • 1 Approximation Algorithms
  • 1 Graph Algorithms
  • 1 Lin-Kernighan algorithm
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact