On the integer-valued variables in the linear vertex packing problem |
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Authors: | Jean-Claude Picard Maurice Queyranne |
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Institution: | (1) Ecole Polytechnique, Montreal, Canada |
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Abstract: | Given a graph with weights on vertices, the vertex packing problem consists of finding a vertex packing (i.e. a set of vertices, no two of them being adjacent) of maximum weight. A linear relaxation of one binary programming formulation of this problem has these two well-known properties: (i) every basic solution is (0, 1/2, 1)-valued, (ii) in an optimum linear solution, an integer-valued variable keeps the same value in an optimum binary solution.As an answer to an open problem from Nemhauser and Trotter, it is shown that there is a unique maximal set of variables which are integral in optimal (VLP) solutions.This research was supported by National Research Council of Canada GRANT A8528 and RD 804. |
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