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A Mixture of Dynamic Programming and Branch-and-Bound for the Subset-Sum Problem


  • Silvano Martello

    (Istituto di Automatica, University of Bologna, Bologna, Italy)

  • Paolo Toth

    (Istituto di Informatica e Sistemistica, University of Firenze, Firenze, Italy)


Given n items, each having a weight w i , and a container of capacity W, the Subset-Sum Problem (SSP) is to select a subset of the items whose total weight is closest to, without exceeding, W. The paper presents a mixed approach (depth first search-dynamic programming) to the exact solution of the problem. An extensive computational experience is presented, comparing the proposed algorithm with that of Ahrens-Finke, as well as with the Balas-Zemel algorithm for large problems. Both "easy" and "hard" problems with values of n up to 10,000 are considered.

Suggested Citation

  • Silvano Martello & Paolo Toth, 1984. "A Mixture of Dynamic Programming and Branch-and-Bound for the Subset-Sum Problem," Management Science, INFORMS, vol. 30(6), pages 765-771, June.
  • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:6:p:765-771

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    Cited by:

    1. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
    2. Dahmani, Isma & Hifi, Mhand & Wu, Lei, 2016. "An exact decomposition algorithm for the generalized knapsack sharing problem," European Journal of Operational Research, Elsevier, vol. 252(3), pages 761-774.


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