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Linear Programming Relaxations of Maxcut
 PROCEEDINGS OF THE 18TH ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 2007
"... It is wellknown that the integrality gap of the usual linear programming relaxation for Maxcut is 2 − ǫ. For general graphs, we prove that for any ǫ and any fixed boundk, adding linear constraints of support bounded by k does not reduce the gap below 2−ǫ. We generalize this to prove that for any ǫ ..."
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Cited by 11 (0 self)
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It is wellknown that the integrality gap of the usual linear programming relaxation for Maxcut is 2 − ǫ. For general graphs, we prove that for any ǫ and any fixed boundk, adding linear constraints of support bounded by k does not reduce the gap below 2−ǫ. We generalize this to prove that for any ǫ
Polytopes of Linear Programming Relaxation for Triangulations
"... Universal polytope is the polytope defined as the convex hull of the characteristic vectors of all triangulations for a given point configuration. The equality system defining this polytope was found, but the system of inequalities are not known yet. Larger polytopes, corresponding to linear pro ..."
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programming relaxations, have been used in practice. We show that (1) the universal polytope, the polytope of relaxation for (2) clique, (3) cocircuit and (4) chamber conditions have inclusion relation in this order. Examples of point configurations for which these polytopes coincide and differ are given
On Linear Programming Relaxations of Hypergraph Matching
, 2009
"... A hypergraph is a generalization of a graph where each hyperedge can contain an arbitrary number of vertices. The hypergraph matching problem is to find a largest collection of disjoint hyperedges. While matching on general graphs is polynomial time solvable, hypergraph matching is NPhard and there ..."
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A hypergraph is a generalization of a graph where each hyperedge can contain an arbitrary number of vertices. The hypergraph matching problem is to find a largest collection of disjoint hyperedges. While matching on general graphs is polynomial time solvable, hypergraph matching is NPhard and there is no good approximation algorithm for the problem in its most general form. We study the restricted case where every hyperedge consists of
Stronger Linear Programming Relaxations of MaxCut
 Mathematical Programming
, 2002
"... We consider linear programming relaxations for the max cut problem in graphs, based on k gonal inequalities. We show that the integrality ratio for random dense graphs is asymptotically 1 + 1=k and for random sparse graphs is at least 1 + 3=k. There are O(n ) kgonal inequalities. These results ..."
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Cited by 9 (1 self)
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We consider linear programming relaxations for the max cut problem in graphs, based on k gonal inequalities. We show that the integrality ratio for random dense graphs is asymptotically 1 + 1=k and for random sparse graphs is at least 1 + 3=k. There are O(n ) kgonal inequalities. These results
Linear programming relaxations and belief propagation – an empirical study
 Jourmal of Machine Learning Research
, 2006
"... The problem of finding the most probable (MAP) configuration in graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method in comput ..."
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Cited by 88 (4 self)
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The problem of finding the most probable (MAP) configuration in graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method
Survivable networks, linear programming relaxations and the parsimonious property
, 1993
"... We consider the survivable network design problem the problem of designing, at minimum cost, a network with edgeconnectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the kedgeconnected network design problem. We establ ..."
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Cited by 54 (11 self)
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establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic
LINEAR PROGRAMMING RELAXATIONS OF QUADRATICALLY CONSTRAINED QUADRATIC PROGRAMS
"... Abstract. We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and principal minors PSD cuts. Computational results based on ..."
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Cited by 12 (1 self)
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Abstract. We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and principal minors PSD cuts. Computational results based
Equivalence of Two Linear Programming Relaxations for Broadcast Scheduling
"... Samir Khuller and YooAh Kim Abstract. A server needs to compute a broadcast schedule for n pages whose request times are known in advance. Outputting a page satisfies all outstanding requests for the page. The goal is to minimize the average waiting time of a client. In this paper we show the equiv ..."
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the equivalence of two apparently different relaxations that have been considered for this problem. Key words: scheduling, broadcasting, approximation algorithms, linear programming 1 Introduction The informal description of the problem is as follows. There are n data items, 1; : : : ; n, called pages. Time
Solution Stability in Linear Programming Relaxations: Graph Partitioning and Unsupervised Learning
"... We propose a new method to quantify the solution stability of a large class of combinatorial optimization problems arising in machine learning. As practical example we apply the method to correlation clustering, clustering aggregation, modularity clustering, and relative performance significance clu ..."
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Cited by 12 (3 self)
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clustering. Our method is extensively motivated by the idea of linear programming relaxations. We prove that when a relaxation is used to solve the original clustering problem, then the solution stability calculated by our method is conservative, that is, it never overestimates the solution stability
Results 1  10
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