Skip to main content
SpringerLink
Log in

Improved approximation algorithms for metric MaxTSP

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

We present two polynomial-time approximation algorithms for the metric case of the maximum traveling salesman problem. One of them is for directed graphs and its approximation ratio is \(\frac{27}{35}\). The other is for undirected graphs and its approximation ratio is \(\frac{7}{8}-o(1)\). Both algorithms improve on the previous bests.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barvinok AI, Johnson DS, Woeginger GJ, Woodroofe R (1998) Finding maximum length tours under polyhedral norms. Proceedings of the Sixth International Conference on Integer Programming and Combinatorial Optimization (IPCO), Lecture Notes in Computer Science 1412:195–201

  • Chen ZZ, Wang L (2005) An improved randomized approximation algorithm for Max TSP. J Comb Optim 9:401–432

    Article  MATH  MathSciNet  Google Scholar 

  • Chen ZZ, Okamoto Y, Wang L (2005) Improved deterministic approximation algorithms for Max TSP. Inf Process Lett 95:333–342

    Article  MathSciNet  Google Scholar 

  • Hassin R, Rubinstein S (2002) A 7/8-Approximation approximations for metric Max TSP. Inf Process Lett 81:247–251

    Article  MATH  MathSciNet  Google Scholar 

  • Kaplan H, Lewenstein M, Shafrir N, Sviridenko M (2003) Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs. Proceeding of the 44th Annual IEEE Symposium on Foundations Computer Science pp 56–75

  • Karp RM, Upfal E, Wigderson A (1986) Constructing a perfect matching is in random NC. Combinatorica 6:35–48

    Article  MATH  MathSciNet  Google Scholar 

  • Kostochka AV, Serdyukov AI (1985) Polynomial algorithms with the estimates \(\frac{3}{4}\) and \(\frac{5}{6}\) for the traveling salesman problem of maximum (in Russian). Upravlyaemye Sistemy 26:55–59

  • Mulmuley K, Vazirani UV, Vazirani VV (1987) Matching is as easy as matrix inversion. Combinatorica 7:105–113

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Tokyo Denki University, Hatoyama, Saitama, 350-0394, Japan

    Zhi-Zhong Chen & Takayuki Nagoya

Authors
  1. Zhi-Zhong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takayuki Nagoya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Zhong Chen.

Additional information

A preliminary version of this paper appeared in the Proceedings of 13th European Symposium on Algorithms (ESA2005), Lecture Notes in Computer Science, Vol. 3669, pp. 179–190, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, ZZ., Nagoya, T. Improved approximation algorithms for metric MaxTSP. J Comb Optim 13, 321–336 (2007). https://doi.org/10.1007/s10878-006-9023-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-006-9023-7

Keywords

Search

Navigation