IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v23y1975i2p207-217.html
   My bibliography  Save this article

When the Greedy Solution Solves a Class of Knapsack Problems

Author

Listed:
  • M. J. Magazine

    (North Carolina State University, Raleigh, North Carolina)

  • G. L. Nemhauser

    (Cornell University, Ithaca, New York)

  • L. E. Trotter

    (Yale University, New Haven, Connecticut)

Abstract

This paper analyzes a heuristic for the knapsack problem that recursively determines a solution by making a variable with smallest marginal unit cost as large as possible. Recursive necessary and sufficient conditions for the optimality of such “greedy” solutions and a “good” algorithm for verifying these conditions are given. Maximum absolute error for nonoptimal “greedy” solutions is also examined.

Suggested Citation

  • M. J. Magazine & G. L. Nemhauser & L. E. Trotter, 1975. "When the Greedy Solution Solves a Class of Knapsack Problems," Operations Research, INFORMS, vol. 23(2), pages 207-217, April.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:2:p:207-217
    DOI: 10.1287/opre.23.2.207
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.23.2.207
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.23.2.207?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. DePaolo, Concetta A. & Rader, David Jr., 2007. "A heuristic algorithm for a chance constrained stochastic program," European Journal of Operational Research, Elsevier, vol. 176(1), pages 27-45, January.
    2. Mathur, Kamlesh & Venkateshan, Prahalad, 2007. "A new lower bound for the linear knapsack problem with general integer variables," European Journal of Operational Research, Elsevier, vol. 178(3), pages 738-754, May.
    3. Yamamoto, Ken, 2014. "Fractal patterns related to dividing coins," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 51-57.
    4. Richard Engelbrecht-Wiggans, 1977. "The Greedy Heuristic Applied to a Class of Set Partitioning and Subset Selection Problems," Cowles Foundation Discussion Papers 469, Cowles Foundation for Research in Economics, Yale University.
    5. Deineko, Vladimir G. & Woeginger, Gerhard J., 2011. "Unbounded knapsack problems with arithmetic weight sequences," European Journal of Operational Research, Elsevier, vol. 213(2), pages 384-387, September.
    6. Steffen Goebbels & Frank Gurski & Jochen Rethmann & Eda Yilmaz, 2017. "Change-making problems revisited: a parameterized point of view," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1218-1236, November.

    More about this item

    Statistics

    Access and download statistics

    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:inm:oropre:v:23:y:1975:i:2:p:207-217. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.