Average case analysis of the set packing problem

• Autorzy: Szkatuła K.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the well known set packing problem and its special case, when the number of subsets is maximized. It is assumed that some of the problem coefficients are realizations of mutually independent random variables. Average case (i.e. asymptotical probabilistic) properties of selected problem characteristics are investigated for the variety of possible instances of the problem.

Słowa kluczowe

EN

Lagrange; set packing problem

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2014
• Tom: Vol. 43, no. 4
• Strony: 557--575
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Szkatuła K.

• Systems Research Institute, Polish Academy of Sciences ul. Newelska 6, 01-447 Warszawa, Poland
• Siedlce University of Natural Sciences and Humanities ul. Konarskiego 2, 08-110 Siedlce, Poland

Bibliografia

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• 2. Averbakh, I. (1994) Probabilistic properties of the dual structure of the multidimensional knapsack problem and fast statistically effcient algorithms. Mathematical Programming, 65, 311–330.
• 3. Garey, M. and Johnson, D. (1972) Computers and Intractability: A Guide to the Theory of NP Completeness. Freeman, San Francisco.
• 4. Karp, R. (1979) Reducibility among combinatorial problems In: R. Miller and J. Thatcher, eds., Complexity of Computer Computations. Plenum Press, New York.
• 5. Martello, S. and Toth, P. (1990) Knapsack Problems: Algorithms and Computer Implementations. Wiley & Sons.
• 6. Meanti, M., Kan, A.R., Stougie, L., and Vercellis, C. (1990) A probabilistic analysis of the multiknapsack value function. Mathematical Programming, 46, 237–247.
• 7. Nemhauser, G. and Wolsey, L. (1988) Integer and Combinatorial Optimization. John Wiley & Sons Inc., New York.
• 8. Szkatula, 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.
• 9. Szkatula, K. (1997) The growth of multi-constraint random knapsacks with large right-hand sides of the constraints. Operations Research Letters, 21, 25–30.
• 10. Vercellis, C. (1986) A probabilistic analysis of the set packing problem. In: Stochastic Programming. Springer Verlag, 272–285.