Skip to main content
SpringerLink
Log in

Deterministic 7/8-Approximation for the Metric Maximum TSP

(Extended Abstract)

  • Conference paper
Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques (APPROX 2008, RANDOM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5171))

Abstract

We present the first 7/8-approximation algorithm for the maximum traveling salesman problem with triangle inequality. Our algorithm is deterministic. This improves over both the randomized algorithm of Hassin and Rubinstein [2] with expected approximation ratio of 7/8 − O(n − 1/2) and the deterministic (7/8 − O(n − 1/3))-approximation algorithm of Chen and Nagoya [1].

In the new algorithm, we extend the approach of processing local configurations using so-called loose-ends, which we introduced in [4].

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen, Z.-Z., Nagoya, T.: Improved approximation algorithms for metric max TSP. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 179–190. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Hassin, R., Rubinstein, S.: A 7/8-approximation algorithm for metric Max TSP. Inf. Process. Lett. 81(5), 247–251 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kostochka, A.V., Serdyukov, A.I.: Polynomial algorithms with the estimates 3/4 and 5/6 for the traveling salesman problem of the maximum (in Russian). Upravlyaemye Sistemy 26, 55–59 (1985)

    MathSciNet  Google Scholar 

  4. Kowalik, Ł., Mucha, M.: 35/44-approximation for asymmetric maximum TSP with triangle inequality. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 589–600. Springer, Heidelberg (2007)

    Google Scholar 

  5. Serdyukov, A.I.: The traveling salesman problem of the maximum (in Russian). Upravlyaemye Sistemy 25, 80–86 (1984)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Poland

    Łukasz Kowalik & Marcin Mucha

Authors
  1. Łukasz Kowalik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcin Mucha
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ashish Goel Klaus Jansen José D. P. Rolim Ronitt Rubinfeld

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kowalik, Ł., Mucha, M. (2008). Deterministic 7/8-Approximation for the Metric Maximum TSP. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2008 2008. Lecture Notes in Computer Science, vol 5171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85363-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85363-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85362-6

  • Online ISBN: 978-3-540-85363-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation