The binested inequalities for the Symmetric Travelling Salesman Polytope

The binested inequalities for the Symmetric Travelling Salesman Polytope

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Article ID: iaor19931584
Country: United States
Volume: 17
Issue: 4
Start Page Number: 882
End Page Number: 900
Publication Date: Nov 1992
Journal: Mathematics of Operations Research
Authors:
Keywords: graphs, networks, sets
Abstract:

This paper defines a family of valid inequalities for the Symmetric Travelling Salesman Polytope which are defined on two nested sets of vertices of the graph. These inequalities generalize the comb inequalities of Chvàtal, Grötschel and Padberg, the clique tree inequalities of Grötschel and Pulleyblank, the path inequalities of Cornuéjols, Fonlupt and Naddef and the hyperstar inequalities of Fleischman. This is the largest known family of valid inequalities known so far. Facet inducing inequalities for the Symmetric Travelling Salesman Polytope contained in this class and in no other one are given proving that this is a proper generalization of the previously mentioned families.

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