Skip to main content
SpringerLink
Log in

Towards Better Inapproximability Bounds for TSP: A Challenge of Global Dependencies

  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9210))

Included in the following conference series:

Abstract

We present in this paper some of the recent techniques and methods for proving best up to now explicit approximation hardness bounds for metric symmetric and asymmetric Traveling Salesman Problem (TSP) as well as related problems of Shortest Superstring and Maximum Compression. We attempt to shed some light on the underlying paradigms and insights which lead to the recent improvements as well as some inherent obstacles for further progress on those problems.

M. Karpinski—Research supported by DFG grants and the Hausdorff grant EXC59-1.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Approximation Taxonomy of Metric TSP (2015). http://theory.cs.uni-bonn.de/info5/tsp

  2. Asadpour, A., Goemans, M., Mądry, A., Gharan, S., Saberi, A.: An \(O(\log n/ \log \log n)\)-approximation algorithm for the asymmetric traveling salesman problem. In: Proceedings of the 21st SODA, pp. 379–389 (2010)

    Google Scholar 

  3. Berman, P., Karpinski, M.: On some tighter inapproximability results. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, p. 200. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  4. Berman, P., Karpinski, M.: Efficient amplifiers and bounded degree optimization. ECCC TR01-053 (2001)

    Google Scholar 

  5. Berman, P., Karpinski, M.: Improved approximation lower bounds on small occurrence optimization. ECCC TR03-008 (2003)

    Google Scholar 

  6. Berman, P., Karpinski, M.: 8/7-approximation algorithm for \((1, 2)\)-TSP. In: Proceedings of the 17th SODA, pp. 641–648 (2006)

    Google Scholar 

  7. Boyd, S., Sitters, R., van der Ster, S., Stougie, L.: TSP on cubic and subcubic graphs. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011. LNCS, vol. 6655, pp. 65–77. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Christofides, N.: Worst-Case Analysis of a New Heuristic for the Traveling Salesman Problem, Technical Report CS-93-13. Carnegie Mellon University, Pittsburgh (1976)

    Google Scholar 

  9. Engebretsen, L.: An explicit lower bound for TSP with distances one and two. Algorithmica 35, 301–318 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Engebretsen, L., Karpinski, M.: TSP with bounded metrics. J. Comput. Syst. Sci. 72, 509–546 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Håstad, J.: Some optimal inapproximability results. J. ACM 48, 798–859 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kaplan, H., Lewenstein, M., Shafrir, N., Sviridenko, M.: Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs. J. ACM 52, 602–626 (2005)

    Article  MathSciNet  Google Scholar 

  13. Karpinski, M.: Approximating bounded degree instances of NP-hard problems. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, p. 24. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Karpinski, M., Lampis, M., Schmied, R.: New inapproximability bounds for TSP. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) Algorithms and Computation. LNCS, vol. 8283, pp. 568–578. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Karpinski, M., Schmied, R.: On approximation lower bounds for TSP with bounded metrics. CoRR abs/1201.5821 (2012)

    Google Scholar 

  16. Karpinski, M., Schmied, R.: Improved lower bounds for the shortest superstring and related problems. In: Proceedings 19th CATS, CRPIT 141, pp. 27–36 (2013)

    Google Scholar 

  17. Karpinski, M., Schmied, R.: Approximation hardness of graphic TSP on cubic graphs, CoRR abs/1304.6800, 2013. Journal version RAIRO-Operations Research 49, pp. 651–668 (2015)

    Google Scholar 

  18. Lampis, M.: Improved inapproximability for TSP. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds.) APPROX 2012 and RANDOM 2012. LNCS, vol. 7408, pp. 243–253. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Mömke, T., Svensson, O.: Approximating graphic TSP by matchings. In: Proceedings of the IEEE 52nd FOCS, pp. 560–569 (2011)

    Google Scholar 

  20. Papadimitriou, C., Vempala, S.: On the approximability of the traveling salesman problem. Combinatorica 26, 101–120 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Papadimitriou, C., Yannakakis, M.: The traveling salesman problem with distances one and two. Math. Oper. Res. 18, 1–11 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  22. Sebő, A., Vygen, J.: Shorter tours by nicer ears: 7/5-approximation for the Graph-TSP, 3/2 for the Path Version, and 4/3 for two-edge-connected subgraphs. Combinatorica 34, 1–34 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and the Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany

    Marek Karpinski

Authors
  1. Marek Karpinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marek Karpinski .

Editor information

Editors and Affiliations

  1. Université Paris Diderot, Paris, France

    Adrian Kosowski

  2. Université Bordeaux 1, Talence, France

    Igor Walukiewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Karpinski, M. (2015). Towards Better Inapproximability Bounds for TSP: A Challenge of Global Dependencies. In: Kosowski, A., Walukiewicz, I. (eds) Fundamentals of Computation Theory. FCT 2015. Lecture Notes in Computer Science(), vol 9210. Springer, Cham. https://doi.org/10.1007/978-3-319-22177-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22177-9_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22176-2

  • Online ISBN: 978-3-319-22177-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation