Have a personal or library account? Click to login
The Two-Constraint Binary Knapsack Problem’s average case analysis for constraints with small, moderate and large coefficients Cover

The Two-Constraint Binary Knapsack Problem’s average case analysis for constraints with small, moderate and large coefficients

Open Access
|Dec 2025

References

  1. Averbakh, I. (1994) Probabilistic properties of the dual structure of the multidimensional knapsack problem and fast statistically efficient algorithms. Mathematical Programming, 65: 311–330.
  2. Frieze, A. and Clarke, M. (1984) Approximation algorithms for the m-dimensional 0-1 knapsack problem: Worst case and probabilistic analysis. European Journal of Operational Research, 15: 100–109.
  3. Garey, M. and Johnson, D. (1970) Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco.
  4. Lee, T.-E. and Oh, G.-T. (1997) The asymptotic value-to-capacity ratio for the multi-class stochastic knapsack problem. European Journal of Operational Research, 103: 584–594.
  5. Loéve, M. (1977) Probability Theory I. Springer Verlag, New York, Heidelberg, Berlin.
  6. Mamer, J. and Schilling, K. (1990) On the growth of random knapsacks. Discrete Applied Mathematics, 28: 223–230.
  7. Martello, S. and Toth, P. (1990) Knapsack Problems: Algorithms and Computer Implementations. Wiley & Sons.
  8. Meanti, M., Kan, A. R., Stougie, L. and Vercellis, C. (1990) A probabilistic analysis of the multiknapsack value function. Mathematical Programming, 46: 237–247.
  9. Nemhauser, G. and Wolsey, L. (1988) Integer and Combinatorial Optimization. John Wiley & Sons Inc., New York.
  10. Schilling, K. (1990) The growth of m-constraint random knapsacks. European Journal of Operational Research, 46: 109–112.
  11. Schilling, K. (1994) Random knapsacks with many constraints. Discrete Applied Mathematics, 48: 163–174.
  12. Szkatu la, K. (1994) On the growth of multi-constraint random knapsacks with various right-hand sides of the constraints. European Journal of Operational Reserch, 73: 199–204.
  13. Szkatu la, K. (1997) The growth of multi-constraint random knapsacks with large right-hand sides of the constraints. Operations Research Letters, 21: 25–30.
  14. Szkatu la, K. (2021) When two-constraint binary knapsack problem is equivalent to classical knapsack problem? In: K. T. Atanassov, V. Atanassova, J. Kacprzyk, A. Ka luszko, M. Krawczak, J. W. Owsiński, S. S. Sotirov,
  15. E. Sotirova, E. Szmidt, and S. Zadrożny, eds., Advances and New Developments in Fuzzy Logic and Technology, Cham, Springer International Publishing, 311–321.
DOI: https://doi.org/10.2478/candc-2025-0007 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569
Language: English
Page range: 205 - 221
Submitted on: Oct 1, 2025
|
Accepted on: Nov 1, 2025
|
Published on: Dec 21, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Krzysztof Szkatuła, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.