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61
An optimal SDP algorithm for MaxCut, . . .
, 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
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 25 (4 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
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
KnapsackBased Cutting Planes for the MaxCut Problem
"... Abstract We present a new procedure for generating cutting planes for the maxcut problem. The procedure consists of three steps. First, we generate a violated (or nearviolated) linear inequality that is valid for the semidefinite programming (SDP) relaxation of the maxcut problem. This can be do ..."
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Abstract We present a new procedure for generating cutting planes for the maxcut problem. The procedure consists of three steps. First, we generate a violated (or nearviolated) linear inequality that is valid for the semidefinite programming (SDP) relaxation of the maxcut problem. This can
Topic: SDP: Maxcut, Max2SAT Date: 03/27/07
"... In this lecture we give SDP (semi definite programming) based algorithms for the Maxcut and ..."
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In this lecture we give SDP (semi definite programming) based algorithms for the Maxcut and
Subsampling Semidefinite Programs and MaxCut on the Sphere
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 129 (2009)
, 2009
"... We study the question of whether the value of mathematical programs such as linear and semidefinite programming hierarchies on a graph G, is preserved when taking a small random subgraph G ′ of G. We show that the value of the GoemansWilliamson (1995) semidefinite program (SDP) for Max Cut of G ′ i ..."
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Cited by 1 (0 self)
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We study the question of whether the value of mathematical programs such as linear and semidefinite programming hierarchies on a graph G, is preserved when taking a small random subgraph G ′ of G. We show that the value of the GoemansWilliamson (1995) semidefinite program (SDP) for Max Cut of G
A MAXCUT FORMULATION OF 0/1 PROGRAMS
"... Abstract. We consider the linear or quadratic 0/1 program for some vectors c ∈ R n , b ∈ Z m , some matrix A ∈ Z m×n and some real symmetric matrix F ∈ R n×n . We show that P can be formulated as a MAXCUT problem whose quadratic form criterion is explicit from the data of P. In particular, to P on ..."
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Abstract. We consider the linear or quadratic 0/1 program for some vectors c ∈ R n , b ∈ Z m , some matrix A ∈ Z m×n and some real symmetric matrix F ∈ R n×n . We show that P can be formulated as a MAXCUT problem whose quadratic form criterion is explicit from the data of P. In particular, to P
Restarting after branching in the SDP approach to MAXCUT and similar combinatorial optimization problems
, 1999
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Results 1  10
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