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International Colloquium on Automata, Languages, and Programming

ICALP 2001: Automata, Languages and Programming pp 201–212Cite as

Approximation Hardness of TSP with Bounded Metrics

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

Abstract

The general asymmetric (and metric) TSP is known to be approximable only to within an O(log n) factor, and is also known to be approximable within a constant factor as soon as the metric is bounded. In this paper we study the asymmetric and symmetric TSP problems with bounded metrics and prove approximation lower bounds of 101/100 and 203/202, respectively, for these problems. We prove also approximation lower bounds of 321/320 and 743/742 for the asymmetric and symmetric TSP with distances one and two.

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References

  1. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and the hardness of approximation problems. J. ACM, 45(3):501–555, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Berman and M. Karpinski. On some tighter inapproximability results. In Proc. 26th ICALP, vol. 1644 of LNCS, pp 200–209, 1999.

    Google Scholar 

  3. H.-J. Böckenhauer, J. Hromkovič, R. Klasing, S. Seibert, and W. Unger. An improved lower bound on the approximability of metric TSP and approximation algorithms for the TSP with sharpened triangle inequality. In Proc. 17th STACS, vol. 1770 of LNCS, pp 382–391, 2000.

    Google Scholar 

  4. H.-J. Böckenhauer and S. Seibert. Improved lower bounds on the approximability of the traveling salesman problem. RAIRO Theoretical Informatics and Applications, 34(3):213–255, 2000.

    Article  MATH  Google Scholar 

  5. N. Christofides. Worst-case analysis of a new heuristic for the traveling salesman problem. Technical Report CS-93-13, GSIA, Carnegie Mellon University, 1976.

    Google Scholar 

  6. L. Engebretsen. An explicit lower bound for TSP with distances one and two. In Proc. 16th STACS, vol. 1563 of LNCS, pp 373–382, 1999.

    Chapter  Google Scholar 

  7. A. Frieze, G. Galbiati, and F. Maffioli. On the worst-case performance of some algorithms for the asymmetric traveling salesman problem. Networks, 12(1):23–39, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. Håstad. Some optimal inapproximability results. In Proc. 29th STOC, pp 1–10, 1997.

    Google Scholar 

  9. R. M. Karp. Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pp 85–103. Plenum Press, New York, 1972.

    Google Scholar 

  10. C. H. Papadimitriou and S. Vempala. On the approximability of the traveling salesman problem. In Proc. 32nd STOC, pp 126–133, 2000.

    Google Scholar 

  11. C. H. Papadimitriou and S. Vempala. On the approximability of the traveling salesman problem. Manuscript, 2001.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. L. Trevisan. When Hamming meets Euclid: The approximability of geometric TSP and MST. In Proc. 29th STOC, pp 21–29, 1997.

    Google Scholar 

  14. S. Vishwanathan. An approximation algorithm for the asymmetric travelling salesman problem with distances one and two. Inf. Process. Lett., 44(6):297–302, 1992.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. MIT Laboratory for Computer Science, 200 Technology Square, NE43-369, Cambridge, Massachusetts, 02139-3594

    Lars Engebretsen

  2. Department of Computer Science, University of Bonn, 53117, Bonn

    Marek Karpinski

Authors
  1. Lars Engebretsen
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  2. Marek Karpinski
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Engebretsen, L., Karpinski, M. (2001). Approximation Hardness of TSP with Bounded Metrics. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_17

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  • DOI: https://doi.org/10.1007/3-540-48224-5_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

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