Set Partitioning and Chain Decomposition

G. L. Nemhauser, L. E. Trotter, Jr. and R. M. Nauss
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G. L. Nemhauser: Department of Operations Research, Cornell University
L. E. Trotter, Jr.: Department of Administrative Sciences, Yale University
R. M. Nauss: Graduate School of Management, University of California, Los Angeles

Management Science, 1974, vol. 20, issue 11, 1413-1423

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.

Date: 1974
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:20:y:1974:i:11:p:1413-1423

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