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Results 1 - 10
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1,723
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 ..."
Abstract
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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
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 Branch-and-Cut me ..."
Abstract
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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
"... ..."
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
Abstract
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical
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 E-GTSP, aris ..."
Abstract
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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
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
Abstract
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
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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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.
The traveling salesman problem
, 1994
"... This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances ..."
Abstract
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Cited by 130 (5 self)
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This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem
On the parsimonious property of relaxations of the symmetric traveling salesman polytope. arXiv/math.CO:blah, submitted
"... ABSTRACT. 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 re ..."
Abstract
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Cited by 1 (1 self)
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ABSTRACT. 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 1 - 10
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