Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Greedy Set-Cover Algorithms

1974–1979; Chvátal, Johnson, Lovász, Stein
  • Neal E. Young
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_175

Keywords and Synonyms

Dominating set; Greedy algorithm; Hitting set; Set cover ; Minimizing a linear function subject to a submodular constraint          

Problem Definition

Given a collection \( { \mathcal{S} } \)


Greedy Algorithm Approximation Ratio Facility Location Problem Submodular Function Good Approximation Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Recommended Reading

  1. 1.
    Brönnimann, H., Goodrich, M.T.: Almost optimal set covers in finite VC-dimension. Discret. Comput. Geom. 14(4), 463–479 (1995)MATHCrossRefGoogle Scholar
  2. 2.
    Chvátal, V.: A greedy heuristic for the set-covering problem. Math. Oper. Res. 4(3), 233–235 (1979)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Lund, C., Yannakakis, M.: On the hardness of approximating minimization problems. J. ACM 41(5), 960–981 (1994)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Feige, U.: A threshold of ln n for approximating set cover. J. ACM 45(4), 634–652 (1998)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Gonzalez, T.F.: Handbook of Approximation Algorithms and Metaheuristics. Chapman & Hall/CRC Computer & Information Science Series (2007)Google Scholar
  6. 6.
    Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9, 256–278 (1974)MATHCrossRefGoogle Scholar
  7. 7.
    Khuller, S., Moss, A., Naor, J.: The budgeted maximum coverage problem. Inform. Process. Lett. 70(1), 39–45 (1999)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Kolliopoulos, S.G., Young, N.E.: Tight approximation results for general covering integer programs. In: Proceedings of the forty-second annual IEEE Symposium on Foundations of Computer Science, pp. 522–528 (2001)Google Scholar
  9. 9.
    Lovász, L.: On the ratio of optimal integral and fractional covers. Discret. Math. 13, 383–390 (1975)MATHCrossRefGoogle Scholar
  10. 10.
    Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, New York (1988)MATHGoogle Scholar
  11. 11.
    van Santen, J.P.H., Buchsbaum, A.L.: Methods for optimal text selection. In: Proceedings of the European Conference on Speech Communication and Technology (Rhodos, Greece) 2, 553–556 (1997)Google Scholar
  12. 12.
    Slavik, P.: A tight analysis of the greedy algorithm for set cover. J. Algorithms 25(2), 237–254 (1997)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Srinivasan, A.: Improved approximations of packing and covering problems. In: Proceedings of the twenty-seventh annual ACM Symposium on Theory of Computing, pp. 268–276 (1995)Google Scholar
  14. 14.
    Stein, S.K.: Two combinatorial covering theorems. J. Comb. Theor. A 16, 391–397 (1974)MATHCrossRefGoogle Scholar
  15. 15.
    Vazirani, V.V.: Approximation Algorithms. Springer, Berlin Heidelberg (2001)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Neal E. Young
    • 1
  1. 1.Department of Computer ScienceUniversity of California at RiversideRiversideUSA