Approximation to the Minimum Rooted Star Cover Problem

  • Wenbo Zhao
  • Peng Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)

Abstract

In this paper, we study the following minimum rooted star cover problem: given a complete graph G = (V, E) with a length function l: E →ℤ +  that satisfies the triangle inequality, a designated root vertex r ∈ V, and a length bound D, the objective is to find a minimum cardinality set of rooted stars, that covers all vertices in V such that the length of each rooted star is at most D, where a rooted star is a subset of E having a common center s ∈ V and containing the edge (r, s). This problem is NP-complete and we present a constant ratio approximation algorithm for this problem.

Keywords

Minimum Rooted Star Cover Approximation Algorithm 

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References

  1. 1.
    Arya, V., et al.: Local Search Heuristics for k-median and Facility Location Problems. In: The proceedings of STOC, pp. 21–29 (2001)Google Scholar
  2. 2.
    Arkin, E.M., Hassin, R., Levin, A.: Approximation for Minimum and Min-Max Vehicle Routing Problems. Journal of Algorithms 59, 1–18 (2006)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Desrochers, M., Desrosiers, J., Solomon, M.: A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows. Operation Research 40, 342–354 (1992)MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Even, G., et al.: Covering Graph Using Trees and Stars. In: Arora, S., et al. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol. 2764, pp. 24–25. Springer, Heidelberg (2003)Google Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco (1979)MATHGoogle Scholar
  6. 6.
    Kohen, A., Kan, A.R., Trienekens, H.: Vehicle Routing with Time Windows. Operations Research 36, 266–273 (1987)Google Scholar
  7. 7.
    Nagarajan, V., Ravi, R.: Minimum vehicle routing with a common deadline. In: Díaz, J., et al. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol. 4110, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Savelsbergh, M.: Local Search for Routing Problems with Time Windows. Annals of Operations Research 4, 285–305 (1985)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Tan, K.C., et al.: Heuristic Methods for Vehicle Routing Problems with Time Windows. Artificial Intelligence in Engineering, 281–295 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Wenbo Zhao
    • 1
    • 2
  • Peng Zhang
    • 1
    • 2
  1. 1.State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, P.O.Box 8718, Beijing, 100080China
  2. 2.Graduate University of Chinese Academy of Sciences, BeijingChina

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