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64
The Symmetric Traveling Salesman Polytope Revisited
, 2001
"... We present in this paper a tour of the symmetric traveling salesman polytope, focusing on inequalities that can be dened on sets of nodes. Most of the widely known inequalities are of this type. Many papers have appeared which give increasingly complex valid inequalities for this polytope, but l ..."
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Cited by 6 (1 self)
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We present in this paper a tour of the symmetric traveling salesman polytope, focusing on inequalities that can be dened on sets of nodes. Most of the widely known inequalities are of this type. Many papers have appeared which give increasingly complex valid inequalities for this polytope
The Domino Inequalities: Facets for the Symmetric Traveling Salesman Polytope
, 2003
"... Adam Letchford defines in [4] the Domino Parity inequalities for the Symmetric Traveling Salesman Polytope (STSP) and gives a polynomial algorithm for the separation of such constraints when the support graph is planar, generalizing a result of Fleischer and Tardos [2] for maximally violated com ..."
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Cited by 3 (1 self)
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Adam Letchford defines in [4] the Domino Parity inequalities for the Symmetric Traveling Salesman Polytope (STSP) and gives a polynomial algorithm for the separation of such constraints when the support graph is planar, generalizing a result of Fleischer and Tardos [2] for maximally violated
A New Polytope for Symmetric Traveling Salesman Problem
"... The classical polytope associated with the symmetric traveling salesman problem (STSP) is usually studied as embedded in the standard subtour elimination polytope. Several classes of facet deflning inequalities of the STSP polytope are used in practical enumeration algorithms. In this paper we cons ..."
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The classical polytope associated with the symmetric traveling salesman problem (STSP) is usually studied as embedded in the standard subtour elimination polytope. Several classes of facet deflning inequalities of the STSP polytope are used in practical enumeration algorithms. In this paper we
On the parsimonious property of relaxations of the symmetric traveling salesman polytope
, 2007
"... We relate the parsimonious property of relaxations of the Symmetric Traveling Salesman Polytope to a connectivity property of the ridge graph of the Graphical Traveling Salesman Polyhedron. This relationship is quite surprising. The proof is elegant and geometric: it makes use of recent results on ..."
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Cited by 1 (1 self)
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We relate the parsimonious property of relaxations of the Symmetric Traveling Salesman Polytope to a connectivity property of the ridge graph of the Graphical Traveling Salesman Polyhedron. This relationship is quite surprising. The proof is elegant and geometric: it makes use of recent results
The Symmetric Generalized Travelling Salesman Polytope
, 1995
"... The symmetric Generalized Travelling Salesman Problem (GTSP) is a variant of the classical symmetric Travelling Salesman Problem, in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster. A different version of the problem, called EGTSP, aris ..."
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Cited by 27 (4 self)
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The symmetric Generalized Travelling Salesman Problem (GTSP) is a variant of the classical symmetric Travelling Salesman Problem, in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster. A different version of the problem, called E
An Analysis of the Asymmetric Quadratic Traveling Salesman Polytope
 SIAM J. Discret. Math
"... Abstract. In the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession. This structure arises, e. g., if the succession of two edges represents energetic conformations, a change of direction or a possible change of transportation means. In the symmet ..."
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Cited by 3 (1 self)
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strengthening approach for lifting valid inequalities of the usual traveling salesman problem to stronger valid inequalities for the symmetric quadratic traveling salesman problem. Applying this strengthening to subtour elimination constraints gives rise to facet defining inequalities, but finding a maximally
A BRANCHANDCUT ALGORITHM FOR THE RESOLUTION OF LARGESCALE SYMMETRIC TRAVELING SALESMAN PROBLEMS
, 1991
"... An algorithm is described for solving largescale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality. The core of the algorithm is a "polyhedral" cuttingplane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the in ..."
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Cited by 205 (7 self)
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An algorithm is described for solving largescale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality. The core of the algorithm is a "polyhedral" cuttingplane procedure that exploits a subset of the system of linear inequalities defining the convex hull
A BranchandCut Algorithm for the Symmetric Generalized Travelling Salesman Problem
, 1995
"... We consider a variant of the classical symmetric Travelling Salesman Problem in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster. This NPhard problem is known in the literature as the symmetric Generalized Travelling Salesman Problem (GT ..."
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Cited by 81 (4 self)
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We consider a variant of the classical symmetric Travelling Salesman Problem in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster. This NPhard problem is known in the literature as the symmetric Generalized Travelling Salesman Problem
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
Lifted cycle inequalities for the asymmetric traveling salesman problem
 Mathematics of Operations Research
, 1999
"... We investigate the family of facet defining inequalities for the asymmetric traveling salesman (ATS) polytope obtainable by lifting the cycle inequalities. We establish several properties of this family that earmark it as the most important among the asymmetric inequalities for the ATS polytope know ..."
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Cited by 2 (1 self)
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We investigate the family of facet defining inequalities for the asymmetric traveling salesman (ATS) polytope obtainable by lifting the cycle inequalities. We establish several properties of this family that earmark it as the most important among the asymmetric inequalities for the ATS polytope
Results 1  10
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