PC-oriented algorithms for the knapsack problem

  • Krzysztof Dudziński
  • Stanisław Walukiewicz
II Mathematical Programming II.2 Discrete Optimization
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


The paper presents branch and bound algorithms for solving 0–1 knapsack problems on personal computers. Some improvements to the existing methods are described and fixed point calculations are introduced. Results of our computational experiment are reported.


knapsack problem branch and bound reduction fixed point calculations 


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  1. E. Balas, E. Zemel (1980), "An Algorithm for Large Zero-One Knapsack Problems", Operations Research 28, 1130–1154.zbMATHMathSciNetCrossRefGoogle Scholar
  2. E. Balas, R. Nauss, E. Zemel (1987), "Comment on Some Computational Results on Real 0–1 Knapsack Problems", Operations Research Letters 6, 139–140.zbMATHCrossRefMathSciNetGoogle Scholar
  3. G.B. Dantzig (1957), "Discrete Variable Extremum Problems", Operations Research 5, 266–277.MathSciNetGoogle Scholar
  4. R.S. Dembo, P.L. Hammer (1980), "A Reduction Algorithm For Knapsack Problems", Methods of Operations Research 36, 49–60.zbMATHMathSciNetGoogle Scholar
  5. K. Dudziński, S. Walukiewicz (1987), "Exact Methods for the Knapsack Problem and its Generalizations", European Journal of Operational Research 28, 3–21.CrossRefMathSciNetzbMATHGoogle Scholar
  6. G.P. Ingargiola, J.F. Korsh (1973), "A Reduction Algorithm for Zero-One Single Knapsack Problems", Management Science 20, 460–463.zbMATHGoogle Scholar
  7. S. Martello, P. Toth (1977), "An Upper Bound for the Zero-One Knapsack Problem and a Branch and Bound Algorithm", European Journal of Operational Research 1, 169–175.zbMATHCrossRefMathSciNetGoogle Scholar
  8. S. Martello, P. Toth (1987), "Algorithms for Knapsack Problems" in S. Martello, G. Laporte, M. Minoux and C. Ribeiro (Eds.), Surveys in Combinatorial Optimization, Annals of Discrete Mathematics 31, North-Holland, Amsterdam.Google Scholar
  9. S. Martello, P. Toth (1988), "A New Algorithm for the 0–1 Knapsack Problem", Management Science 34, 633–641.zbMATHMathSciNetGoogle Scholar
  10. D. Pisinger, S. Walukiewicz (1989), "Experiments with 0–1 Knapsack Algorithms", Research Report, Systems Research Institute Polish, Academy of Sciences, Warsaw.Google Scholar
  11. P. Toth (1980), "Dynamic Programming Algorithms for the Zero-One Knapsack Problem", Computing 25, 29–45.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Krzysztof Dudziński
    • 1
  • Stanisław Walukiewicz
    • 1
  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland

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