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A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2009, RANDOM 2009)

Abstract

We give a deterministic combinatorial 7/9-approximation algorithm for the symmetric maximum traveling salesman problem.

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References

  1. Barvinok, A., Gimadi, E.K., Serdyukov, A.I.: The maximun traveling salesman problem. In: Gutin, G., Punnen, A. (eds.) The Traveling Salesman Problem and its variations, pp. 585–607. Kluwer, Dordrecht (2002)

    Google Scholar 

  2. Bhatia, R.: Private communication

    Google Scholar 

  3. Bläser, M., Ram, L.S., Sviridenko, M.: Improved Approximation Algorithms for Metric Maximum ATSP and Maximum 3-Cycle Cover Problems. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 350–359. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Chen, Z.-Z., Okamoto, Y., Wang, L.: Improved deterministic approximation algorithms for Max TSP. Information Processing Letters 95, 333–342 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, Z.-Z., Nagoya, T.: Improved approximation algorithms for metric Max TSP. J.Comb. Optim. 13, 321–336 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Engebretsen, L.: An explicit lower bound for TSP with distances one and two. Algorithmica 35(4), 301–319 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Engebretsen, L., Karpinski, M.: Approximation hardness of TSP with bounded metrics. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 201–212. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  8. Fisher, M.L., Nemhauser, G.L., Wolsey, L.A.: An analysis of approximation for finding a maximum weight Hamiltonian circuit. Oper. Res. 27, 799–809 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hassin, R., Rubinstein, S.: Better Approximations for Max TSP. Information Processing Letters 75, 181–186 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hassin, R., Rubinstein, S.: A 7/8-approximation algorithm for metric Max TSP. Information Processing Letters 81(5), 247–251 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kaplan, H., Lewenstein, M., Shafrir, N., Sviridenko, M.: Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regualar Multigraphs. J. ACM 52(4), 602–626 (2005)

    Article  MathSciNet  Google Scholar 

  12. Kosaraju, S.R., Park, J.K., Stein, C.: Long tours and short superstrings. In: Proc. 35th Annual Symposium on Foundations of Computer Science (FOCS), pp. 166–177 (1994)

    Google Scholar 

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

    MathSciNet  Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Kowalik, Ł., Mucha, M.: Deterministic 7/8-approximation for the metric maximum TSP. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 132–145. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Papadimitriou, C.H., Yannakakis, M.: The traveling salesman problem with distances one and two. Mathematics of Operations Research 18(1), 1–11 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  17. Schrijver, A.: Nonbipartite Matching and Covering. In: Combinatorial Optimization, vol. A, pp. 520–561. Springer, Heidelberg (2003)

    Google Scholar 

  18. Serdyukov, A.I.: An Algorithm with an Estimate for the Traveling Salesman Problem of Maximum (in Russian). Upravlyaemye Sistemy 25, 80–86 (1984)

    MathSciNet  MATH  Google Scholar 

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Paluch, K., Mucha, M., Ma̧dry, A. (2009). A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_23

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  • DOI: https://doi.org/10.1007/978-3-642-03685-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03684-2

  • Online ISBN: 978-3-642-03685-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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