2010
DOI: 10.1007/978-3-642-13036-6_23
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Extending SDP Integrality Gaps to Sherali-Adams with Applications to Quadratic Programming and MaxCutGain

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Cited by 10 publications
(7 citation statements)
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“…This implicitly contains most known sophisticated approximation algorithms for many problems including SparsestCut and MaximumSatisifiability. Indeed, serveral very strong negative results of this type have been obtained (see [1,3,9,12,14,21,22,36,[38][39][40]42] and others). These are also viewed as lower bounds of approximability in certain restricted models of computation.How strong are these restricted models of computation?…”
mentioning
confidence: 91%
“…This implicitly contains most known sophisticated approximation algorithms for many problems including SparsestCut and MaximumSatisifiability. Indeed, serveral very strong negative results of this type have been obtained (see [1,3,9,12,14,21,22,36,[38][39][40]42] and others). These are also viewed as lower bounds of approximability in certain restricted models of computation.How strong are these restricted models of computation?…”
mentioning
confidence: 91%
“…For the level k = 1 (i.e. the "Adams-Sherali + SDP hierarchy") some negative results in this direction have been provided in Benabbas and Magen [2], and in Benabbas et al [3].…”
Section: Practical and Computational Considerationsmentioning
confidence: 99%
“…On the other hand, for 0/1 problems and for the parameter value k = 1, the hierarchy (3.5) is what is called the Sherali-Adams + SDP hierarchy (basic SDP-relaxation + RLT hierarchy) in e.g. Benabas and Magen [3] and Benabbas et al [2]; and in [3,2] the authors show that any (constant) level d of this hierarchy, viewed as a strengthening of the basic SDP-relaxation, does not make the integrality gap decrease.…”
Section: Sherali-adams' Rlt For 0/1 Programsmentioning
confidence: 99%
“…Thus every optimization problem on P can be reformulated as an optimization problem over any extension of P . This is why extended formulations are interesting for optimization: in (2), the number of constraints in the right-hand side can be much smaller than the number of constraints in the left-hand side.…”
Section: Introductionmentioning
confidence: 99%
“…Lower bounds on restricted types of extended formulations have been studied by quite many authors, starting with the work of Yannakakis [32] on symmetric extended formulations. There has been work on hierarchies such as the Sherali-Adams [29] and Lovász-Schrijver hierarchies [23], see, e.g., [9,26,16,11,19,2]; further work on symmetric extended formulations [21,25,6] and also work on extended formulations from low variance protocols [15].…”
Section: Introductionmentioning
confidence: 99%