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An optimal SDP algorithm for Max-Cut, . . .

by Ryan O'Donnell, Yi Wu , 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

by Subhash Khot, Ryan O'Donnell , 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., ..."
Abstract - Cited by 25 (4 self) - Add to MetaCart
(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

by Yi Wu, Yi Wu , 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

Knapsack-Based Cutting Planes for the Max-Cut Problem

by Adam N Letchford , Konstantinos Kaparis
"... 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

by Scribe Siddharth, Barman Lecturer, Shuchi Chawla
"... 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

by Boaz Barak, Moritz Hardt, Thomas Holenstein, David Steurer - 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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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

by Jean B Lasserre
"... 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

A STRENGTHENED SDP RELAXATION via a SECOND LIFTING for the MAX-CUT PROBLEM

by Miguel F. Anjos , Henry Wolkowicz , 1999
"... ..."
Abstract - Cited by 16 (7 self) - Add to MetaCart
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Restarting after branching in the SDP approach to MAX-CUT and similar combinatorial optimization problems

by John E. Mitchell , 1999
"... ..."
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SpeeDP: A new algorithm to compute the SDP relaxations of Max-Cut for very large graphs

by L. Grippo, L. Palagi, M. Piacentini, V. Piccialli, G. Rinaldi , 2010
"... ..."
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