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The symmetric traveling salesman polytope: New facets from the graphical relaxation
 MATHEMATICS OF OPERATIONS RESEARCH
, 2007
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SUBDIVIDING THE POLAR OF A FACE
, 708
"... ABSTRACT. Let S be a convex polytope. The set of all valid inequalities carries the structure of a convex polytope S △ , called the polar (polytope) of S. The facial structure of the polar provides information for each of its points: two points a and b are in the same face of S △ if and only if the ..."
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ABSTRACT. Let S be a convex polytope. The set of all valid inequalities carries the structure of a convex polytope S △ , called the polar (polytope) of S. The facial structure of the polar provides information for each of its points: two points a and b are in the same face of S △ if and only if the faces of S obtained by intersecting it with the hyperplanes given respectively by a and b coincide. Suppose now that S is a face of another polyhedron P. Then the points of S △ carry some additional information: the set of faces of P which one can obtain by “rotating” the hyperplane given by a point. This additional information is captured by the structure of a polyhedral complex subdividing S △. In this paper, we study this subdivision for the following examples: The Birkhoff polytope as a face of the matching polytope; the permutahedron as a facet of another permutahedron; the Symmetric Traveling Salesman Polytope, also known as Hamiltonian Cycle polytope, as a face of the connected Eulerian multigraph polyhedron, also known as Graphical Traveling Salesman Polyhedron. 1.
ON THE FACIAL STRUCTURE OF SYMMETRIC AND GRAPHICAL TRAVELING SALESMAN POLYHEDRA
, 2009
"... The Symmetric Traveling Salesman Polytope Sn for a fixed number n of cities is a face of the corresponding Graphical Traveling Salesman Polyhedron Pn. This has been used to study facets of Sn using Pn as a tool. In this paper, we study the operation of “rotating” (or “lifting”) valid inequalities fo ..."
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The Symmetric Traveling Salesman Polytope Sn for a fixed number n of cities is a face of the corresponding Graphical Traveling Salesman Polyhedron Pn. This has been used to study facets of Sn using Pn as a tool. In this paper, we study the operation of “rotating” (or “lifting”) valid inequalities for Sn to obtain a valid inequalities for Pn. As an application, we describe a surprising relationship between (a) the parsimonious property of relaxations of the Symmetric Traveling Salesman Polytope and (b) a connectivity property of the ridge graph of the Graphical Traveling Salesman Polyhedron.