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Connected Set Cover Problem and Its Applications

  • Tian-Ping Shuai
  • Xiao-Dong Hu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4041)

Abstract

We study an extension of the set cover problem, the connected set cover problem, the problem is to find a set cover of minimal size that satisfies some connectivity constraint. We first propose two algorithms that find optimal solutions for two cases, respectively, and then we propose one approximation algorithm for a special case that has the best possible performance ratio. At last we consider how to apply the obtained result to solve a wavelength assignment problem in all optical networks.

Keywords

Set cover Approximation algorithm Performance ratio Wavelength assignment 

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References

  1. 1.
    Briers, A.: Incorporating connectivity into reserve selection procedures. Biological Conservation 14, 342–355 (2000)CrossRefGoogle Scholar
  2. 2.
    Chvátal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4, 233–235 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Feige, U.: A threshold of ln n for aproximating set cover. In: Proc. 28th ACM Symposium on Theory of Computing, pp. 314–318 (1996)Google Scholar
  4. 4.
    Johnson, D.S.: Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences 9, 256–278 (1974)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Possingham, H., Ball, I., Andelman, S.: Mathematical methods for representative reserve networks. In: Ferson, S., Burgman, M. (eds.) Quantitative Methods for Conservation Biology, pp. 291–306. Springer, New York (2000)CrossRefGoogle Scholar
  6. 6.
    Ramaswami, R., Sasaki, G.: Multiwavelength optical networks with limited wavelength conversion. IEEE/ACM Transactions on Networking 6(6), 744–754 (1998)CrossRefGoogle Scholar
  7. 7.
    Ruan, L., Du, D.-Z., Hu, X.-D., Jia, X.-H., Li, D.-Y., Sun, Z.: Converter placement supporting broadcast in WDM networks. IEEE Transactions on Computers 50(7), 750–758 (2001)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tian-Ping Shuai
    • 1
  • Xiao-Dong Hu
    • 2
  1. 1.Department of MathematicsBeijing University of Post and Telecom.BeijingChina
  2. 2.Institute of Applied MathematicsChinese Academy of SciencesBeijingChina

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