The Parameterized Complexity of Local Search for TSP, More Refined

  • Jiong Guo
  • Sepp Hartung
  • Rolf Niedermeier
  • Ondřej Suchý
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

We extend previous work on the parameterized complexity of local search for the Travelling Salesperson Problem (TSP). So far, its parameterized complexity has been investigated with respect to the distance measures (which define the local search area) “Edge Exchange” and “Max-Shift”. We perform studies with respect to the distance measures “Swap” and “m-Swap”, “Reversal” and “m-Reversal”, and “Edit”, achieving both fixed-parameter tractability and W[1]-hardness results. Moreover, we provide non-existence results for polynomial-size problem kernels and we show that some in general W[1]-hard problems turn fixed-parameter tractable when restricted to planar graphs.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balas, E.: New classes of efficiently solvable generalized traveling salesman problems. Ann. Oper. Res. 86, 529–558 (1999)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bodlaender, H.L.: Kernelization: New Upper and Lower Bound Techniques. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 17–37. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Bodlaender, H.L., Downey, R.G., Fellows, M.R., Hermelin, D.: On Problems Without Polynomial Kernels. J. Comput. System Sci. 75(8), 423–434 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Caprara, A.: Sorting by reversals is difficult. In: Proc. 1st RECOMB, pp. 75–83. ACM Press (1997)Google Scholar
  5. 5.
    Chen, J., Chor, B., Fellows, M., Huang, X., Juedes, D.W., Kanj, I.A., Xia, G.: Tight lower bounds for certain parameterized NP-hard problems. Inform. and Comput. 201(2), 216–231 (2005)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Deineko, V.G., Woeginger, G.J.: A study of exponential neighborhoods for the travelling salesman problem and for the quadratic assignment problem. Math. Program., Ser. A 87(3), 519–542 (2000)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  8. 8.
    Fellows, M.R., Hermelin, D., Rosamond, F.A., Vialette, S.: On the parameterized complexity of multiple-interval graph problems. Theor. Comput. Sci. 410(1), 53–61 (2009)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Fellows, M.R., Rosamond, F.A., Fomin, F.V., Lokshtanov, D., Saurabh, S., Villanger, Y.: Local Search: Is Brute-Force Avoidable? In: Proc. 21th IJCAI, pp. 486–491 (2009)Google Scholar
  10. 10.
    Flum, J., Grohe, M.: Parameterized complexity and subexponential time. Bulletin of the EATCS 84, 71–100 (2004)MathSciNetMATHGoogle Scholar
  11. 11.
    Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. SIGACT News 38(1), 31–45 (2007)CrossRefGoogle Scholar
  12. 12.
    Gutin, G., Punnen, A.: The Traveling Salesman Problem and its Variations. Combinatorial Optimization (2002)Google Scholar
  13. 13.
    Johnson, D.S., McGeoch, L.A.: Experimental analysis of heuristics for the STSP. In: The Traveling Salesman Problem and its Variations, pp. 369–443 (2004)Google Scholar
  14. 14.
    Krokhin, A., Marx, D.: On the hardness of losing weight. ACM Trans. Algorithms (to appear, 2011) (online available)Google Scholar
  15. 15.
    Marx, D.: Searching the k-change neighborhood for TSP is W[1]-hard. Oper. Res. Lett. 36(1), 31–36 (2008)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Marx, D., Schlotter, I.: Stable assignment with couples: Parameterized complexity and local search. Discrete Optim. 8(1), 25–40 (2011)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jiong Guo
    • 1
  • Sepp Hartung
    • 2
  • Rolf Niedermeier
    • 2
  • Ondřej Suchý
    • 1
  1. 1.Universität des SaarlandesSaarbrückenGermany
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

Personalised recommendations