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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

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 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
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
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
The Hungarian method for the assignment problem
 Naval Res. Logist. Quart
, 1955
"... Assuming that numerical scores are available for the performance of each of n persons on each of n jobs, the "assignment problem" is the quest for an assignment of persons to jobs so that the sum of the n scores so obtained is as large as possible. It is shown that ideas latent in the work ..."
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Cited by 1238 (0 self)
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Assuming that numerical scores are available for the performance of each of n persons on each of n jobs, the "assignment problem" is the quest for an assignment of persons to jobs so that the sum of the n scores so obtained is as large as possible. It is shown that ideas latent in the work of two Hungarian mathematicians may be exploited to yield a new method of solving this problem. 1.
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

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, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
The traveling salesman problem
, 1994
"... This paper presents a selfcontained 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 ..."
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Cited by 130 (5 self)
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This paper presents a selfcontained 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
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
Concentration Of Measure And Isoperimetric Inequalities In Product Spaces
, 1995
"... . The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product# N of probability spaces has measure at least one half, "most" of the points of# N are "close" to A. We proceed to a systematic exploration of this phenomenon. The meaning ..."
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Cited by 383 (4 self)
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. The meaning of the word "most" is made rigorous by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work "close" is defined in three main ways, each of them giving rise to related, but di#erent inequalities. The inequalities are all proved
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