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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
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Yamamoto, Ken, 2014. "Fractal patterns related to dividing coins," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 51-57.
    5. 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.
    6. Yang Yang, 2024. "An Improved Unbounded-DP Algorithm for the Unbounded Knapsack Problem with Bounded Coefficients," Mathematics, MDPI, vol. 12(12), pages 1-12, June.
    7. 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.

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