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Average case analysis of the set packing problem
Subtitle:Raport Badawczy = Research Report ; RB/58/2014
Creator: Publisher:Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences
Place of publishing: Date issued/created: Description:557-575 stron ; 21 cm ; Bibliografia s. 575
Abstract: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. The important results of the paper are: • Behavior of the optimal solution values of the set packing problem is presented for the special asymptotic case, where mutual asymptotical relation between m (number of elements of the packed set) and n (number of sets provided) is playing an essential role. • Probability of reaching feasible solution is reasonably high (i.e. ≥ 2/e, 2/e ≈ 0.736); moreover, it may be set arbitrarily close to 1 (e.g. 0.999), although the deterioration in the quality of approximation of the behavior of the optimal solution values may be substantial. • Some relations between the general case of the set packing problem and its maximization for the special case are investigated.
Relation:Raport Badawczy = Research Report
Resource type: Detailed Resource Type: Source: Language: Language of abstract: Rights:Licencja Creative Commons Uznanie autorstwa 4.0
Terms of use:Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -
Digitizing institution:Instytut Badań Systemowych Polskiej Akademii Nauk
Original in:Biblioteka Instytutu Badań Systemowych PAN
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