An Improved Approximation Algorithm for the Bandpass Problem

  • Weitian Tong
  • Randy Goebel
  • Wei Ding
  • Guohui Lin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7285)

Abstract

The general Bandpass-B problem is NP-hard and can be approximated by a reduction into the B-set packing problem, with a worst case performance ratio of O(B 2). When B = 2, a maximum weight matching gives a 2-approximation to the problem. The Bandpass-2 problem, or simply the Bandpass problem, can be viewed as a variation of the maximum traveling salesman problem, in which the edge weights are dynamic rather than given at the front. We present in this paper a \(\frac{36}{19}\)-approximation algorithm for the Bandpass problem, which is the first improvement over the simple maximum weight matching based 2-approximation algorithm.

Keywords

Bandpass problem approximation algorithm edge coloring maximum weight matching worst case performance ratio 

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References

  1. 1.
    Arkin, E.M., Hassin, R.: On local search for weighted packing problems. Mathematics of Operations Research 23, 640–648 (1998)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Babayev, D.A., Bell, G.I., Nuriyev, U.G.: The bandpass problem: combinatorial optimization and library of problems. Journal of Combinatorial Optimization 18, 151–172 (2009)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Bell, G.I., Babayev, D.A.: Bandpass problem. In: Annual INFORMS Meeting, Denver, CO, USA (October 2004)Google Scholar
  4. 4.
    Chandra, B., Halldórsson, M.M.: Greedy local improvement and weighted set packing approximation. In: ACM-SIAM Proceedings of the Tenth Annual Symposium on Discrete Algorithms (SODA 1999), pp. 169–176 (1999)Google Scholar
  5. 5.
    Chen, Z.-Z., Okamoto, Y., Wang, L.: Improved deterministic approximation algorithms for Max TSP. Information Processing Letters 95, 333–342 (2005)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman and Company, San Francisco (1979)MATHGoogle Scholar
  7. 7.
    Hassin, R., Rubinstein, S.: Better approximations for Max TSP. Information Processing Letters 75, 181–186 (2000)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Lin, G.: On the Bandpass problem. Journal of Combinatorial Optimization 22, 71–77 (2011)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Paluch, K., Mucha, M., Mądry, A.: A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX 2009. LNCS, vol. 5687, pp. 298–311. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Serdyukov, A.I.: An algorithms for with an estimate for the traveling salesman problem of the maximum. Upravlyaemye Sistemy 25, 80–86 (1984)MathSciNetMATHGoogle Scholar
  11. 11.
    Vizing, V.G.: On an estimate of the chromatic class of a p-graph. Diskretnogo Analiza 3, 25–30 (1964)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Weitian Tong
    • 1
  • Randy Goebel
    • 1
  • Wei Ding
    • 2
  • Guohui Lin
    • 1
  1. 1.Department of Computing ScienceUniversity of AlbertaEdmontonCanada
  2. 2.Zhejiang Water Conservancy and Hydropower CollegeHangzhouChina

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