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Results 1 - 10
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61
An optimal SDP algorithm for Max-Cut, . . .
, 2007
"... Let G be an undirected graph for which the standard Max-Cut 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 Max-Cut 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 UGC-hardness for Max-Cut-Gain
, 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 Max-Cut SDP based on Euclidean space with the Gaussian probability distribution. This shows that the SDP-rounding algorithm of Charikar-Wirth 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 Max-Cut 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 Max-Cut 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
Knapsack-Based Cutting Planes for the Max-Cut Problem
"... Abstract We present a new procedure for generating cutting planes for the max-cut problem. The procedure consists of three steps. First, we generate a violated (or near-violated) linear inequality that is valid for the semidefinite programming (SDP) relaxation of the max-cut problem. This can be do ..."
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Abstract We present a new procedure for generating cutting planes for the max-cut problem. The procedure consists of three steps. First, we generate a violated (or near-violated) linear inequality that is valid for the semidefinite programming (SDP) relaxation of the max-cut problem. This can
Topic: SDP: Max-cut, Max-2-SAT Date: 03/27/07
"... In this lecture we give SDP (semi definite programming) based algorithms for the Max-cut and ..."
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In this lecture we give SDP (semi definite programming) based algorithms for the Max-cut and
Subsampling Semidefinite Programs and Max-Cut 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 Goemans-Williamson (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 Goemans-Williamson (1995) semidefinite program (SDP) for Max Cut of G
A MAX-CUT 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 MAX-CUT 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 MAX-CUT problem whose quadratic form criterion is explicit from the data of P. In particular, to P
Restarting after branching in the SDP approach to MAX-CUT and similar combinatorial optimization problems
, 1999
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