IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v238y2016i1p229-24110.1007-s10479-015-2069-0.html
   My bibliography  Save this article

A-priori upper bounds for the set covering problem

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-015-2069-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-015-2069-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    6. 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.
    7. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Gao, Chao & Yao, Xin & Weise, Thomas & Li, Jinlong, 2015. "An efficient local search heuristic with row weighting for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 750-761.
    3. Owais, Mahmoud & Moussa, Ghada S. & Hussain, Khaled F., 2019. "Sensor location model for O/D estimation: Multi-criteria meta-heuristics approach," Operations Research Perspectives, Elsevier, vol. 6(C).
    4. 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.
    5. Li, Shengyin & Huang, Yongxi, 2014. "Heuristic approaches for the flow-based set covering problem with deviation paths," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 144-158.
    6. Masoud Yaghini & Mohammad Karimi & Mohadeseh Rahbar, 2015. "A set covering approach for multi-depot train driver scheduling," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 636-654, April.
    7. Wang, Yiyuan & Pan, Shiwei & Al-Shihabi, Sameh & Zhou, Junping & Yang, Nan & Yin, Minghao, 2021. "An improved configuration checking-based algorithm for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 294(2), pages 476-491.
    8. Jee Eun Kang & Will Recker, 2015. "Strategic Hydrogen Refueling Station Locations with Scheduling and Routing Considerations of Individual Vehicles," Transportation Science, INFORMS, vol. 49(4), pages 767-783, November.
    9. Abdullah Alshehri & Mahmoud Owais & Jayadev Gyani & Mishal H. Aljarbou & Saleh Alsulamy, 2023. "Residual Neural Networks for Origin–Destination Trip Matrix Estimation from Traffic Sensor Information," Sustainability, MDPI, vol. 15(13), pages 1-21, June.
    10. Victor Reyes & Ignacio Araya, 2021. "A GRASP-based scheme for the set covering problem," Operational Research, Springer, vol. 21(4), pages 2391-2408, December.
    11. Lakmali Weerasena & Aniekan Ebiefung & Anthony Skjellum, 2022. "Design of a heuristic algorithm for the generalized multi-objective set covering problem," Computational Optimization and Applications, Springer, vol. 82(3), pages 717-751, July.
    12. Naji-Azimi, Zahra & Toth, Paolo & Galli, Laura, 2010. "An electromagnetism metaheuristic for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 205(2), pages 290-300, September.
    13. Jordi Pereira & Igor Averbakh, 2013. "The Robust Set Covering Problem with interval data," Annals of Operations Research, Springer, vol. 207(1), pages 217-235, August.
    14. Shane N. Hall & Sheldon H. Jacobson & Edward C. Sewell, 2008. "An Analysis of Pediatric Vaccine Formulary Selection Problems," Operations Research, INFORMS, vol. 56(6), pages 1348-1365, December.
    15. Jans, Raf & Degraeve, Zeger, 2008. "A note on a symmetrical set covering problem: The lottery problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 104-110, April.
    16. Davidov, Sreten & Pantoš, Miloš, 2017. "Planning of electric vehicle infrastructure based on charging reliability and quality of service," Energy, Elsevier, vol. 118(C), pages 1156-1167.
    17. R. Baldacci & E. Hadjiconstantinou & A. Mingozzi, 2004. "An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation," Operations Research, INFORMS, vol. 52(5), pages 723-738, October.
    18. Song, Zhe & Kusiak, Andrew, 2010. "Mining Pareto-optimal modules for delayed product differentiation," European Journal of Operational Research, Elsevier, vol. 201(1), pages 123-128, February.
    19. Seona Lee & Sang-Ho Lee & HyungJune Lee, 2020. "Timely directional data delivery to multiple destinations through relay population control in vehicular ad hoc network," International Journal of Distributed Sensor Networks, , vol. 16(5), pages 15501477209, May.
    20. Alireza Amirteimoori & Simin Masrouri, 2021. "DEA-based competition strategy in the presence of undesirable products: An application to paper mills," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 5-21.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:238:y:2016:i:1:p:229-241:10.1007/s10479-015-2069-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.