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All 01 polytopes are traveling salesman polytopes
 Combinatorica
, 1996
"... We study the facial structure of two important permutation polytopes ..."
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Cited by 13 (0 self)
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We study the facial structure of two important permutation polytopes
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
 In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (FOCS’96
, 1996
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes a ..."
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Cited by 399 (3 self)
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Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes
Traveling Salesman Problems With Profits: An Overview
 Transportation Science
, 2001
"... Traveling Salesman Problems with Profits (TSPs with Profits) are a generalization of the Traveling Salesman Problem (TSP) where it is not necessary to visit all vertices. With each vertex is associated a profit. The objective is to find a route with a satisfying collected profit (maximized) and trav ..."
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Cited by 74 (2 self)
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Traveling Salesman Problems with Profits (TSPs with Profits) are a generalization of the Traveling Salesman Problem (TSP) where it is not necessary to visit all vertices. With each vertex is associated a profit. The objective is to find a route with a satisfying collected profit (maximized
On the Graphical Relaxation of the Symmetric Traveling Salesman
, 2007
"... The Graphical Traveling Salesman Polyhedron (GTSP) has been proposed by Naddef and Rinaldi to be viewed as a relaxation of the Symmetric Traveling Salesman Polytope (STSP). It has also been employed by Applegate, Bixby, Chvátal, and Cook for solving the latter to optimality by the BranchandCut me ..."
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Cited by 3 (3 self)
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The Graphical Traveling Salesman Polyhedron (GTSP) has been proposed by Naddef and Rinaldi to be viewed as a relaxation of the Symmetric Traveling Salesman Polytope (STSP). It has also been employed by Applegate, Bixby, Chvátal, and Cook for solving the latter to optimality by the Branch
The symmetric traveling salesman polytope: New facets from the graphical relaxation
 MATHEMATICS OF OPERATIONS RESEARCH
, 2007
"... ..."
A Graduated Assignment Algorithm for Graph Matching
, 1996
"... A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational comp ..."
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Cited by 378 (16 self)
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A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twentyfive thousand experiments conducted on 100 node random graphs of varying types (graphs with only zeroone links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have...
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 204 (6 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
THE GRAPHICAL TRAVELING SALESMAN POLYHEDRON IS THE INTERSECTION OF THE POSITIVE ORTHANT WITH THE MINKOWSKI SUM OF THE SYMMETRIC TRAVELING SALESMAN POLYTOPE AND THE POLAR OF THE METRIC CONE
, 2008
"... In this short communication, we observe that the Graphical Traveling Salesman Polyhedron is the intersection of the positive orthant with the Minkowski sum of the Symmetric Traveling Salesman Polytope and the polar of the metric cone. This follows trivially from known facts. There are two reasons wh ..."
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Cited by 1 (1 self)
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In this short communication, we observe that the Graphical Traveling Salesman Polyhedron is the intersection of the positive orthant with the Minkowski sum of the Symmetric Traveling Salesman Polytope and the polar of the metric cone. This follows trivially from known facts. There are two reasons
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 75 (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
Results 11  20
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7,356