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SDP gaps and UGChardness for MaxCutGain
, 2008
"... Given a graph with maximum cut of (fractional) size c, the Goemans–Williamson semidefinite programming (SDP)based algorithm is guaranteed to find a cut of size at least.878 · c. However this guarantee becomes trivial when c is near 1/2, since making random cuts guarantees a cut of size 1/2 (i.e., ..."
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Cited by 26 (3 self)
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(ε/log(1/ε)) integrality gap for the MaxCut SDP based on Euclidean space with the Gaussian probability distribution. This shows that the SDProunding algorithm of CharikarWirth is essentially best possible. 2. We show how this SDP gap can be translated into a Long Code test with the same parameters
Maxcut Problem
, 2007
"... Maxcut problem is one of many NPhard graph theory problems which attracted many researchers over the years. Though there is almost no hope in finding a polynomialtime algorithm for maxcut problem, various heuristics, or combination of optimization and heuristic methods have been developed to solv ..."
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Maxcut problem is one of many NPhard graph theory problems which attracted many researchers over the years. Though there is almost no hope in finding a polynomialtime algorithm for maxcut problem, various heuristics, or combination of optimization and heuristic methods have been developed
Semidefinite Relaxations for MaxCut
 The Sharpest Cut, Festschrift in Honor of M. Padberg's 60th Birthday. SIAM
, 2001
"... We compare several semidefinite relaxations for the cut polytope obtained by applying the lift and project methods of Lov'asz and Schrijver and of Lasserre. We show that the tightest relaxation is obtained when aplying the Lasserre construction to the node formulation of the maxcut problem. Th ..."
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Cited by 11 (2 self)
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We compare several semidefinite relaxations for the cut polytope obtained by applying the lift and project methods of Lov'asz and Schrijver and of Lasserre. We show that the tightest relaxation is obtained when aplying the Lasserre construction to the node formulation of the maxcut problem
by
, 2007
"... Let G be an undirected graph for which the standard MaxCut SDP relaxation achieves at least a c fraction of the total edge weight, 1 2 ≤ c ≤ 1. If the actual optimal cut for G is at most an s fraction of the total edge weight, we say that (c, s) is an SDP gap. We define the SDP gap curve GapSDP: [ ..."
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Let G be an undirected graph for which the standard MaxCut SDP relaxation achieves at least a c fraction of the total edge weight, 1 2 ≤ c ≤ 1. If the actual optimal cut for G is at most an s fraction of the total edge weight, we say that (c, s) is an SDP gap. We define the SDP gap curve GapSDP
by
, 2007
"... Let G be an undirected graph for which the standard MaxCut SDP relaxation achieves at least a c fraction of the total edge weight, 1 2 ≤ c ≤ 1. If the actual optimal cut for G is at most an s fraction of the total edge weight, we say that (c, s) is an SDP gap. We define the SDP gap curve GapSDP: [ ..."
Abstract
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Let G be an undirected graph for which the standard MaxCut SDP relaxation achieves at least a c fraction of the total edge weight, 1 2 ≤ c ≤ 1. If the actual optimal cut for G is at most an s fraction of the total edge weight, we say that (c, s) is an SDP gap. We define the SDP gap curve GapSDP
Approximation Algorithm for the MaxCut Problem
 Combinatorics, Probability and Computing
, 1993
"... In this project, we investigated several approximation algorithms for the MaxCut problem. ..."
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Cited by 5 (0 self)
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In this project, we investigated several approximation algorithms for the MaxCut problem.
Randomized Heuristics for the MaxCut Problem
 Optimization Methods and Software
, 2002
"... Given an undirected graph with edge weights, the MAXCUT problem consists in finding a partition of the nodes into two subsets, such that the sum of the weights of the edges having endpoints in different subsets is maximized. ..."
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Cited by 40 (17 self)
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Given an undirected graph with edge weights, the MAXCUT problem consists in finding a partition of the nodes into two subsets, such that the sum of the weights of the edges having endpoints in different subsets is maximized.
Lagrangian Smoothing Heuristics for MaxCut
, 2002
"... This paper presents a smoothing heuristic for an NPhard combinatorial problem. Starting with a convex Lagrangian relaxation, a pathfollowing method is applied to obtain good solutions while gradually transforming the relaxed problem into the original problem formulated with an exact penalty functio ..."
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Cited by 5 (2 self)
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This paper presents a smoothing heuristic for an NPhard combinatorial problem. Starting with a convex Lagrangian relaxation, a pathfollowing method is applied to obtain good solutions while gradually transforming the relaxed problem into the original problem formulated with an exact penalty function. Starting points are drawn using different sampling techniques that use randomization and eigenvectors. The dual point that defines the convex relaxation is computed via eigenvalue optimization using subgradient techniques. The proposed method turns out to be competitive with the most recent ones. The idea presented here is generic and can be generalized to all boxconstrained problems where convex Lagrangian relaxation can be applied. Furthermore, to the best of our knowledge, this is the first time that a Lagrangian heuristic is combined with pathfollowing techniques. Key words. semidefinite programming, quadratic programming, combinatorial optimization, nonconvex programming, approximation methods and heuristics, pathfollowing, AMS classifications. 90C22, 90C20, 90C27, 90C26, 90C59 2 1
Results 1  10
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