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138
Treewidth and the SheraliAdams operator
, 2003
"... We describe a connection between the treewidth of graphs and the SheraliAdams reformulation procedure for 0/1 integer programs. For the case of vertex packing problems, our main result can be restated as follows: let G be a graph, let k 1 and let x be a feasible vector for the formulation ..."
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Cited by 6 (0 self)
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We describe a connection between the treewidth of graphs and the SheraliAdams reformulation procedure for 0/1 integer programs. For the case of vertex packing problems, our main result can be restated as follows: let G be a graph, let k 1 and let x be a feasible vector for the formulation
TreewidthBased Conditions for Exactness Of The SheraliAdams and Lasserre Relaxations
, 2004
"... The SheraliAdams (SA) and Lasserre (LS) approaches are "liftandproject" methods that generate nested sequences of linear and/or semidefinite relaxations of an arbitrary 01 polytope . Although both procedures are known to terminate with an exact description of P after n steps, th ..."
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Cited by 14 (3 self)
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The SheraliAdams (SA) and Lasserre (LS) approaches are "liftandproject" methods that generate nested sequences of linear and/or semidefinite relaxations of an arbitrary 01 polytope . Although both procedures are known to terminate with an exact description of P after n steps
Robust algorithms for Max Independent Set on Minorfree graphs based on the SheraliAdams Hierarchy
"... Abstract. This work provides a Linear Programmingbased Polynomial Time Approximation Scheme (PTAS) for two classical NPhard problems on graphs when the input graph is guaranteed to be planar, or more generally Minor Free. The algorithm applies a sufficiently large number (some function of 1/ɛ when ..."
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Cited by 2 (1 self)
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when 1 + ɛ approximation is required) of rounds of the socalled SheraliAdams LiftandProject system. needed to obtain a (1 + ɛ)approximation, where f is some function that depends only on the graph that should be avoided as a minor. The problem we discuss are the wellstudied problems, the Max
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
The Linear Programming Polytope of Binary Constraint Problems with Bounded TreeWidth
"... Abstract. We show how to efficiently model binary constraint problems (BCP) as integer programs. After considering treestructured BCPs first, we show that a SheraliAdamslike procedure results in a polynomialsize linear programming description of the convex hull of all integer feasible solutions ..."
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Cited by 2 (1 self)
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Abstract. We show how to efficiently model binary constraint problems (BCP) as integer programs. After considering treestructured BCPs first, we show that a SheraliAdamslike procedure results in a polynomialsize linear programming description of the convex hull of all integer feasible solutions
Approximate Inference in Graphical Models using LP Relaxations
, 2010
"... Graphical models such as Markov random fields have been successfully applied to a wide variety of fields, from computer vision and natural language processing, to computational biology. Exact probabilistic inference is generally intractable in complex models having many dependencies between the vari ..."
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Cited by 27 (1 self)
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the variables. We present new approaches to approximate inference based on linear programming (LP) relaxations. Our algorithms optimize over the cycle relaxation of the marginal polytope, which we show to be closely related to the first lifting of the SheraliAdams hierarchy, and is significantly tighter than
Narrow proofs may be maximally long
 In Proceedings of the 29th IEEE Conference on Computational Complexity
, 2014
"... We prove that there are 3CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size nΩ(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size nO(w) is essentially tight. Moreover, our low ..."
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Cited by 4 (3 self)
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lower bound generalizes to polynomial calculus resolution (PCR) and SheraliAdams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. Our results do not extend all the way to Lasserre, however, where the formulas we study have proofs of constant rank
Narrow proofs may be . . .
"... We prove that there are 3CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size nΩ(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size nO(w) is essentially tight. Moreover, our lo ..."
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lower bounds can be generalized to polynomial calculus resolution (PCR) and SheraliAdams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. Our results do not extend all the way to Lasserre, however—the formulas we study have Lasserre proofs of constant
Sparsest cut on bounded treewidth graphs: Algorithms and hardness results
 In 45th Annual ACM Symposium on Symposium on Theory of Computing
, 2013
"... We give a 2approximation algorithm for NonUniform Sparsest Cut that runs in time nO(k), where k is the treewidth of the graph. This improves on the previous 22 kapproximation in time poly(n)2O(k) due to Chlamtác ̌ et al. [CKR10]. To complement this algorithm, we show the following hardness resul ..."
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Cited by 4 (0 self)
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hard to approximate better than 17/16 − ε for ε> 0; assuming the Unique Games Conjecture the hardness becomes 1/αGW − ε. For graphs with large (but constant) treewidth, we show a hardness result of 2 − ε assuming the Unique Games Conjecture. Our algorithm rounds a linear program based on (a subset of) the SheraliAdams
Tight SizeDegree Bounds for SumsofSquares Proofs
, 2015
"... We exhibit families of 4CNF formulas over n variables that have sumsofsquares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) d but require SOS proofs of size nΩ(d) for values of d = d(n) from constant all the way up to nδ for some universal constant δ. This shows that the nO(d) running ..."
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] to obtain size lower bounds for the proof systems resolution, polynomial calculus, and SheraliAdams from lower bounds on width, degree, and rank, respectively.
Results 1  10
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138