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SDP Gaps from Pairwise Independence
"... This work considers the problem of approximating fixed predicate constraint satisfaction problems (MAX kCSP(P)). We show that if the set of assignments accepted by P contains the support of a balanced pairwise independent distribution over the domain of the inputs, then such a problem on n variable ..."
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Cited by 6 (0 self)
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This work considers the problem of approximating fixed predicate constraint satisfaction problems (MAX kCSP(P)). We show that if the set of assignments accepted by P contains the support of a balanced pairwise independent distribution over the domain of the inputs, then such a problem on n variables cannot be approximated better than the trivial (random) approximation, even after augmenting the natural semidefinite relaxation with Ω(n) levels of the SheraliAdams hierarchy. It was recently shown [3] that under the Unique Game Conjecture, CSPs for predicates satisfying this condition cannot be approximated better than the trivial approximation. Our results can be viewed as an unconditional analogue of this result in a restricted computational model. We also introduce a new generalization of techniques to define consistent “local distributions” over partial assignments to variables in the problem, which is often the crux of proving lower bounds for such hierarchies.
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
SDP gaps for 2to1 and other LabelCover variants
"... Abstract. In this paper we present semidefinite programming (SDP) gap instances for the following variants of the LabelCover problem, closely related to the Unique Games Conjecture: (i) 2to1 LabelCover; (ii) 2to2 LabelCover; (iii) αconstraint LabelCover. All of our gap instances have perfec ..."
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Cited by 2 (0 self)
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Abstract. In this paper we present semidefinite programming (SDP) gap instances for the following variants of the LabelCover problem, closely related to the Unique Games Conjecture: (i) 2to1 LabelCover; (ii) 2to2 LabelCover; (iii) αconstraint LabelCover. All of our gap instances have
SDP gaps and UGC hardness for multiway cut, 0extension and . . .
"... The connection between integrality gaps and computational hardness of discrete optimization problems is an intriguing question. In recent years, this connection has prominently figured in several tight UGCbased hardness results. We show in this paper a direct way of turning integrality gaps into ha ..."
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The connection between integrality gaps and computational hardness of discrete optimization problems is an intriguing question. In recent years, this connection has prominently figured in several tight UGCbased hardness results. We show in this paper a direct way of turning integrality gaps
Estimating Wealth Effects without Expenditure Data— or Tears
 Policy Research Working Paper 1980, The World
, 1998
"... Abstract: We use the National Family Health Survey (NFHS) data collected in Indian states in 1992 and 1993 to estimate the relationship between household wealth and the probability a child (aged 6 to 14) is enrolled in school. A methodological difficulty to overcome is that the NFHS, modeled closely ..."
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Cited by 871 (16 self)
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, produces internally coherent results, and provides a close correspondence with State Domestic Product (SDP) and poverty rates data. We validate the asset index using data from Indonesia, Pakistan and Nepal which contain data on both consumption expenditures and asset ownership. The asset index has
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
Integrality gaps for strong SDP relaxations of unique games
"... Abstract — With the work of Khot and Vishnoi [18] as a starting point, we obtain integrality gaps for certain strong SDP relaxations of Unique Games. Specifically, we exhibit a Unique Games gap instance for the basic semidefinite program strengthened by all valid linear inequalities on the inner pro ..."
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Cited by 38 (7 self)
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Abstract — With the work of Khot and Vishnoi [18] as a starting point, we obtain integrality gaps for certain strong SDP relaxations of Unique Games. Specifically, we exhibit a Unique Games gap instance for the basic semidefinite program strengthened by all valid linear inequalities on the inner
SDP integrality gaps with local ℓ1embeddability
 In Proc. 50 th IEEE FOCS
, 2009
"... We construct integrality gap instances for SDP relaxation of the MAXIMUM CUT and the SPARSEST CUT problems. If the triangle inequality constraints are added to the SDP, then the SDP vectors naturally define an npoint negative type metric where n is the number of vertices in the problem instance. Ou ..."
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Cited by 12 (4 self)
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We construct integrality gap instances for SDP relaxation of the MAXIMUM CUT and the SPARSEST CUT problems. If the triangle inequality constraints are added to the SDP, then the SDP vectors naturally define an npoint negative type metric where n is the number of vertices in the problem instance
Polynomial integrality gaps for strong SDP relaxations of Densest ksubgraph
"... The Densest ksubgraph problem (i.e. find a size k subgraph with maximum number of edges), is one of the notorious problems in approximation algorithms. There is a significant gap between known upper and lower bounds for Densest ksubgraph: the current best algorithm gives an ≈ O(n 1/4) approximatio ..."
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Cited by 14 (4 self)
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include: • A lower bound of Ω ( n 1/4 / log 3 n) on the integrality gap for Ω(log n / log log n) rounds of the SheraliAdams relaxation for Densest ksubgraph. This also holds for the relaxation obtained from SheraliAdams with an added SDP constraint. Our gap instances are in
A (log n)Ω(1) integrality gap for the Sparsest Cut SDP
 In Proceedings of 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009
, 2009
"... ar ..."
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