Improved Inapproximability for TSP

  • Michael Lampis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7408)

Abstract

The Traveling Salesman Problem is one of the most studied problems in computational complexity and its approximability has been a long standing open question. Currently, the best known inapproximability threshold known is \(\frac{220}{219}\) due to Papadimitriou and Vempala. Here, using an essentially different construction and also relying on the work of Berman and Karpinski on bounded occurrence CSPs, we give an alternative and simpler inapproximability proof which improves the bound to \(\frac{185}{184}\).

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References

  1. 1.
    Berman, P., Karpinski, M.: On Some Tighter Inapproximability Results (Extended Abstract). In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 200–209. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Berman, P., Karpinski, M.: Efficient amplifiers and bounded degree optimization. Electronic Colloquium on Computational Complexity (ECCC) 8(53) (2001)Google Scholar
  3. 3.
    Berman, P., Karpinski, M.: Improved approximation lower bounds on small occurrence optimization. Electronic Colloquium on Computational Complexity (ECCC) 10(008) (2003)Google Scholar
  4. 4.
    Böckenhauer, H.-J., Hromkovič, J., Klasing, R., Seibert, S., Unger, W.: An Improved Lower Bound on the Approximability of Metric TSP and Approximation Algorithms for the TSP with Sharpened Triangle Inequality. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 382–394. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Engebretsen, L.: An explicit lower bound for TSP with distances one and two. Algorithmica 35(4), 301–318 (2003)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Gharan, S.O., Saberi, A., Singh, M.: A randomized rounding approach to the traveling salesman problem. In: Ostrovsky [12], pp. 550–559Google Scholar
  7. 7.
    Håstad, J.: Some optimal inapproximability results. Journal of the ACM (JACM) 48(4), 798–859 (2001)MATHCrossRefGoogle Scholar
  8. 8.
    Karpinski, M., Schmied, R.: On approximation lower bounds for TSP with bounded metrics. CoRR, abs/1201.5821 (2012)Google Scholar
  9. 9.
    Lampis, M.: Improved Inapproximability for TSP. CoRR, abs/1206.2497 (2012)Google Scholar
  10. 10.
    Mömke, T., Svensson, O.: Approximating graphic TSP by matchings. In: Ostrovsky [12], pp. 560–569Google Scholar
  11. 11.
    Mucha, M.: 13/9-approximation for graphic TSP. In: Dürr, C., Wilke, T. (eds.) STACS. LIPIcs, vol. 14, pp. 30–41. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2012)Google Scholar
  12. 12.
    Ostrovsky, R. (ed.): IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, USA, October 22-25. IEEE (2011)Google Scholar
  13. 13.
    Papadimitriou, C.H., Vempala, S.: On the approximability of the traveling salesman problem (extended abstract). In: Yao, F.F., Luks, E.M. (eds.) STOC, pp. 126–133. ACM (2000)Google Scholar
  14. 14.
    Papadimitriou, C.H., Vempala, S.: On the approximability of the traveling salesman problem. Combinatorica 26(1), 101–120 (2006)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Papadimitriou, C.H., Yannakakis, M.: The traveling salesman problem with distances one and two. Mathematics of Operations Research, 1–11 (1993)Google Scholar
  16. 16.
    Sebö, A., Vygen, J.: Shorter tours by nicer ears: CoRR, abs/1201.1870 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael Lampis
    • 1
  1. 1.KTH Royal Institue of TechnologySweden

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