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Set Partitioning and Chain Decomposition

Set Partitioning and Chain Decomposition There is given a finite set I and a family of subsets of I. We consider the problem of determining a minimum cardinality subfamily that is a partition of I. A branch-and-bound algorithm is presented. The bounds are obtained by determining chain decompositions of directed acyclic graphs. The computation time required to determine a bound is bounded by a polynomial in the cardinality of I. Some computational experience is reported and relationships with other methods are discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Management Science INFORMS

Set Partitioning and Chain Decomposition

Management Science , Volume 20 (11): 11 – Jul 1, 1974
12 pages

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Publisher
INFORMS
Copyright
Copyright © INFORMS
Subject
Research Article
ISSN
0025-1909
eISSN
1526-5501
DOI
10.1287/mnsc.20.11.1413
Publisher site
See Article on Publisher Site

Abstract

There is given a finite set I and a family of subsets of I. We consider the problem of determining a minimum cardinality subfamily that is a partition of I. A branch-and-bound algorithm is presented. The bounds are obtained by determining chain decompositions of directed acyclic graphs. The computation time required to determine a bound is bounded by a polynomial in the cardinality of I. Some computational experience is reported and relationships with other methods are discussed.

Journal

Management ScienceINFORMS

Published: Jul 1, 1974

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