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A linear round lower bound for lovaszschrijver sdp relaxations of vertex cover
 In IEEE Conference on Computational Complexity. IEEE Computer Society
, 2006
"... We study semidefinite programming relaxations of Vertex Cover arising from repeated applications of the LS+ “liftandproject ” method of Lovasz and Schrijver starting from the standard linear programming relaxation. Goemans and Kleinberg prove that after one round of LS+ the integrality gap remains ..."
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Cited by 30 (9 self)
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We study semidefinite programming relaxations of Vertex Cover arising from repeated applications of the LS+ “liftandproject ” method of Lovasz and Schrijver starting from the standard linear programming relaxation. Goemans and Kleinberg prove that after one round of LS+ the integrality gap
LovászSchrijver Reformulation
, 2010
"... We discuss the hierarchies of linear and semidefinite programs defined by Lovász and Schrijver [29]. We describe recent progress on these hierarchies in the contexts of algorithm design, computational complexity and proof complexity. ..."
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Cited by 2 (0 self)
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We discuss the hierarchies of linear and semidefinite programs defined by Lovász and Schrijver [29]. We describe recent progress on these hierarchies in the contexts of algorithm design, computational complexity and proof complexity.
New lower bounds for Approximation Algorithms in the LovaszSchrijver Hierarchy
, 2006
"... Determining how well we can efficiently compute approximate solutions to NPhard problems is of great theoretical and practical interest. Typically the famous PCP theorem is used for showing that a problem has no algorithms computing good approximations. Unfortunately, for many problem this approach ..."
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Cited by 4 (0 self)
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has failed. Nevertheless, for such problems, we may instead be able to show that a large subclass of algorithms cannot compute good approximations. This thesis takes this approach, concentrating on subclasses of algorithms defined by the LS and LS+ LovászSchrijver hierarchies. These subclasses define
New lower bounds for Vertex Cover in the LovászSchrijver hierarchy
, 2006
"... Lovász and Schrijver [13] defined three progressively stronger procedures LS0, LS and LS+, for systematically tightening linear relaxations over many rounds. All three procedures yield the integral hull after at most n rounds. On the other hand, constant rounds of LS+ can derive the relaxations be ..."
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Cited by 16 (1 self)
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that the integrality gap for VERTEX COVER relaxations remains 2−o(1) even after Ω(log n) rounds LS. However, their method can only prove round lower bounds as large as the girth of the input graph, which is O(log n) for interesting graphs. We break through this “girth barrier ” and show that the integrality gap
Integrality gaps of 2 − o(1) for vertex cover sdps in the lovászschrijver hierarchy
 IN: ECCCTR: ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, TECHNICAL REPORTS
, 2006
"... Linear and semidefinite programming are highly successful approaches for obtaining good approximations for NPhard optimization problems. For example, breakthrough approximation algorithms for MAX CUT and SPARSEST CUT use semidefinite programming. Perhaps the most prominent NPhard problem whose e ..."
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Cited by 15 (6 self)
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, there is a widespread belief that SDP techniques are the most promising methods available for improving upon this factor of 2. Following a line of study initiated by Arora et al. [3], our aim is to show that a large family of LP and SDP based algorithms fail to produce an approximation for VERTEX COVER
Tight Integrality Gaps for LovászSchrijver LP Relaxations of Vertex Cover and Max Cut
 PROCEEDINGS OF THE 39TH SYMPOSIUM ON ACM SYMPOSIUM ON THEORY OF COMPUTING
, 2007
"... We study linear programming relaxations of Vertex Cover and Max Cut arising from repeated applications of the “liftandproject ” method of Lovasz and Schrijver starting from the standard linear programming relaxation. For Vertex Cover, Arora, Bollobas, Lovasz and Tourlakis prove that the integralit ..."
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Cited by 29 (9 self)
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We study linear programming relaxations of Vertex Cover and Max Cut arising from repeated applications of the “liftandproject ” method of Lovasz and Schrijver starting from the standard linear programming relaxation. For Vertex Cover, Arora, Bollobas, Lovasz and Tourlakis prove
Exponential lower bounds and Integrality Gaps for Treelike LovászSchrijver Procedures
, 2007
"... The matrix cuts of Lovász and Schrijver are methods for tightening linear relaxations of zeroone programs by the addition of new linear inequalities. We address the question of how many new inequalities are necessary to approximate certain combinatorial problems with strong guarantees, and to solve ..."
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Cited by 10 (1 self)
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vertex cover to a factor better than 7/6. We prove exponential size lower bounds for treelike LovászSchrijver proofs of unsatisfiability for several prominent unsatisfiable CNFs, including random 3CNF formulas, random systems of linear equations, and the Tseitin graph formulas. Furthermore, we prove
The probable value of the LovaszSchrijver relaxations for maximum independent set
 SIAM Journal on Computing
, 2003
"... independent set ..."
Lower bounds for LovászSchrijver systems and beyond follow from multiparty communication complexity
, 2006
"... ..."
A comparison of the SheraliAdams, LovászSchrijver and Lasserre relaxations for 01 programming
 Mathematics of Operations Research
, 2001
"... ..."
Results 1  10
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