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A-priori upper bounds for the set covering problem

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  • Giovanni Felici
  • Sokol Ndreca
  • Aldo Procacci
  • Benedetto Scoppola

Abstract

In this paper we present a new bound obtained with the probabilistic method for the solution of the set covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic results, and it depends only on the number of rows of the coefficient matrix and the row densities. We also consider the particular case of matrices that are almost block decomposable, and show how the bound may improve according to the particular decomposition adopted. Such final result may provide interesting indications for comparing different matrix decomposition strategies. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Giovanni Felici & Sokol Ndreca & Aldo Procacci & Benedetto Scoppola, 2016. "A-priori upper bounds for the set covering problem," Annals of Operations Research, Springer, vol. 238(1), pages 229-241, March.
    • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:p:229-241:10.1007/s10479-015-2069-0
    DOI: 10.1007/s10479-015-2069-0
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    References listed on IDEAS

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    1. Grossman, Tal & Wool, Avishai, 1997. "Computational experience with approximation algorithms for the set covering problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 81-92, August.
    2. Lan, Guanghui & DePuy, Gail W. & Whitehouse, Gary E., 2007. "An effective and simple heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1387-1403, February.
    3. Burke, Edmund K. & Curtois, Tim, 2014. "New approaches to nurse rostering benchmark instances," European Journal of Operational Research, Elsevier, vol. 237(1), pages 71-81.
    4. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    5. Nicos Christofides & S. Korman, 1975. "Note--A Computational Survey of Methods for the Set Covering Problem," Management Science, INFORMS, vol. 21(5), pages 591-599, January.
    6. Endre Boros & Andrea Scozzari & Fabio Tardella & Pierangela Veneziani, 2014. "Polynomially Computable Bounds for the Probability of the Union of Events," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1311-1329, November.
    7. C.N. Vijeyamurthy & R. Panneerselvam, 2010. "Literature review of covering problem in operations management," International Journal of Services, Economics and Management, Inderscience Enterprises Ltd, vol. 2(3/4), pages 267-285.
    8. Alberto Caprara & Paolo Toth & Matteo Fischetti, 2000. "Algorithms for the Set Covering Problem," Annals of Operations Research, Springer, vol. 98(1), pages 353-371, December.
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