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1,014
Superpolynomial lower bounds for monotone span programs
, 1996
"... In this paper we obtain the first superpolynomial lower bounds for monotone span programs computing explicit functions. The best previous lower bound was Ω(n 5/2) by Beimel, Gál, Paterson [BGP]; our proof exploits a general combinatorial lower bound criterion from that paper. Our lower bounds are ba ..."
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Cited by 48 (6 self)
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are based on an analysis of Paleytype bipartite graphs via Weil’s character sum estimates. We prove an n Ω(log n / log log n) lower bound for the size of monotone span programs for the clique problem. Our results give the first superpolynomial lower bounds for linear secret sharing schemes. We demonstrate
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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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
Improving Exhaustive Search Implies Superpolynomial Lower Bounds
, 2009
"... The P vs NP problem arose from the question of whether exhaustive search is necessary for problems with short verifiable solutions. We do not know if even a slight algorithmic improvement over exhaustive search is universally possible for all NP problems, and to date no major consequences have been ..."
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Cited by 40 (7 self)
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be extremely difficult (if not impossible). We also prove unconditional superpolynomial timespace lower bounds for improving on exhaustive search: there is a problem verifiable with k(n) length witnesses in O(n a) time (for some a and some function k(n) ≤ n) that cannot be solved in k(n) c n a+o(1) time
TimeSpace Tradeoffs in Resolution: Superpolynomial Lower Bounds For Superlinear Space
 STOC'12
, 2012
"... We give the first timespace tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size N that have Resolution refutations of space and size each roughly N log2 N (and like all formulas have Resolution refutations of space N) ..."
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Cited by 14 (1 self)
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We give the first timespace tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size N that have Resolution refutations of space and size each roughly N log2 N (and like all formulas have Resolution refutations of space N
Every monotone graph property is testable
 Proc. of STOC 2005
, 2005
"... A graph property is called monotone if it is closed under removal of edges and vertices. Many monotone graph properties are some of the most wellstudied properties in graph theory, and the abstract family of all monotone graph properties was also extensively studied. Our main result in this paper i ..."
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Cited by 52 (9 self)
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A graph property is called monotone if it is closed under removal of edges and vertices. Many monotone graph properties are some of the most wellstudied properties in graph theory, and the abstract family of all monotone graph properties was also extensively studied. Our main result in this paper
Finite Limits and Monotone Computations: The Lower Bounds Criterion
 Proc. of the 12th IEEE Conference on Computational Complexity
, 1997
"... Our main result is a combinatorial lower bounds criterion for monotone circuits over the reals. We allow any unbounded fanin nondecreasing realvalued functions as gates. The only requirement is their "locality ". Unbounded fanin AND and OR gates, as well as any threshold gate T m s (x ..."
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Cited by 5 (1 self)
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Our main result is a combinatorial lower bounds criterion for monotone circuits over the reals. We allow any unbounded fanin nondecreasing realvalued functions as gates. The only requirement is their "locality ". Unbounded fanin AND and OR gates, as well as any threshold gate T m s (x
Fast Approximation Algorithms for Fractional Packing and Covering Problems
, 1995
"... This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed ..."
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Cited by 263 (13 self)
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This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques
Graph Complexity Measures and Monotonicity
, 2012
"... The structural complexity of instances of computational problems has been an important research area in theoretical computer science in the last decades. Its success manifested itself in treewidth—a complexity measure for undirected graphs. Many practically relevant problems that are difficult in g ..."
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Cited by 2 (2 self)
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in general, can be efficiently solved on graphs of bounded treewidth. For directed graphs, there are several similar measures, among others entanglement, directed treewidth, DAGwidth and Kellywidth, that have shown their advantages as well as disadvantages. In this thesis, we work on complexity measures
Combinatorics of Monotone Computations
 Combinatorica
, 1998
"... Our main result is a combinatorial lower bounds criterion for a general model of monotone circuits, where we allow as gates: (i) arbitrary monotone Boolean functions whose minterms or maxterms (or both) have length 6 d, and (ii) arbitrary realvalued nondecreasing functions on 6 d variables. This r ..."
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Cited by 8 (4 self)
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to Sipser. We demonstrate the criterion by superpolynomial lower bounds for explicit Boolean functions, associated with bipartite Paley graphs and partial tdesigns. We then derive exponential lower bounds for cliquelike graph functions of Tardos, thus establishing an exponential gap between the monotone
Results 1  10
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