Subtitle:

Raport Badawczy = Research Report ; RB/58/2014

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Description:

557-575 pages ; 21 cm ; Bibliography p. 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

Detailed Resource Type:

Report

Resource Identifier:

oai:rcin.org.pl:217479

Source:

RB-2014-58

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open