, Volume 8, Issue 1, pp 232248
First online:
Vertex packings: Structural properties and algorithms
 G. L. NemhauserAffiliated withCornell University
 , L. E. TrotterJr.Affiliated withYale University
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We consider a binary integer programming formulation (VP) for the weighted vertex packing problem in a simple graph. A sufficient “local” optimality condition for (VP) is given and this result is used to derive relations between (VP) and the linear program (VLP) obtained by deleting the integrality restrictions in (VP). Our most striking result is that those variables which assume binary values in an optimum (VLP) solution retain the same values in an optimum (VP) solution. This result is of interest because variables are (0, 1/2, 1). valued in basic feasible solutions to (VLP) and (VLP) can be solved by a “good” algorithm. This relationship and other optimality conditions are incorporated into an implicit enumeration algorithm for solving (VP). Some computational experience is reported.
 Title
 Vertex packings: Structural properties and algorithms
 Journal

Mathematical Programming
Volume 8, Issue 1 , pp 232248
 Cover Date
 197512
 DOI
 10.1007/BF01580444
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 G. L. Nemhauser ^{(1)}
 L. E. Trotter Jr. ^{(2)}
 Author Affiliations

 1. Cornell University, Ithaca, N.Y., USA
 2. Yale University, New Haven, Conn., USA