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188,085
Sharp Thresholds of Graph properties, and the ksat Problem
 J. Amer. Math. Soc
, 1998
"... Given a monotone graph property P , consider p (P ), the probability that a random graph with edge probability p will have P . The function d p (P )=dp is the key to understanding the threshold behavior of the property P . We show that if d p (P )=dp is small (corresponding to a nonsharp thres ..."
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Cited by 214 (7 self)
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Given a monotone graph property P , consider p (P ), the probability that a random graph with edge probability p will have P . The function d p (P )=dp is the key to understanding the threshold behavior of the property P . We show that if d p (P )=dp is small (corresponding to a non
The Asymptotic Order of the Random kSAT Threshold
 In Proc. FOCS
, 2002
"... Form a random kSAT formula on n variables by selecting uniformly and independently m = rn clauses out of all 2 possible kclauses. The Satisfiability Threshold Conjecture asserts that for each k there exists a constant r k such that, as n tends to infinity, the probability that the formula is sa ..."
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Cited by 44 (13 self)
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Form a random kSAT formula on n variables by selecting uniformly and independently m = rn clauses out of all 2 possible kclauses. The Satisfiability Threshold Conjecture asserts that for each k there exists a constant r k such that, as n tends to infinity, the probability that the formula
Thresholds for Random Geometric kSAT
, 2013
"... We study two geometric models of random ksatisfiability which combine random kSAT with the Random Geometric Graph: boolean literals are placed uniformly at random or according to a Poisson process in a cube, and for each set of k literals contained in a ball of a given radius, a clause is formed. ..."
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We study two geometric models of random ksatisfiability which combine random kSAT with the Random Geometric Graph: boolean literals are placed uniformly at random or according to a Poisson process in a cube, and for each set of k literals contained in a ball of a given radius, a clause is formed
Satisfiability threshold of the skewed random kSAT
 In Proceedings, 7th Intl. Conf. on Theory and Applications of Satisfiability Testing
, 2004
"... Abstract. We consider the satisfiability phase transition in skewed random kSAT distributions. It is known that the random kSAT model, in which the instance is a set of m kclauses selected uniformly from the set of all kclauses over n variables, has a satisfiability phase transition at a certain ..."
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Cited by 2 (0 self)
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Abstract. We consider the satisfiability phase transition in skewed random kSAT distributions. It is known that the random kSAT model, in which the instance is a set of m kclauses selected uniformly from the set of all kclauses over n variables, has a satisfiability phase transition at a
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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o(1)) ln n), and previous results of Lund and Yannakakis, that showed hardness of approximation within a ratio of (log 2 n)=2 ' 0:72 lnn. For max kcover we show an approximation threshold of (1 \Gamma 1=e) (up to low order terms), under the assumption that P != NP .
A fast iterative shrinkagethresholding algorithm with application to . . .
, 2009
"... We consider the class of Iterative ShrinkageThresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast Iterat ..."
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Cited by 1055 (8 self)
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We consider the class of Iterative ShrinkageThresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast
Bounds on thresholds of regular random kSAT
 Accepted to International Conference on Theory and Applications of Satisfiability Testing (SAT
, 2010
"... ar ..."
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
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Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
Random kSAT: two moments suffice to cross a sharp threshold
 CoRR
, 2006
"... Abstract. Many NPcomplete constraint satisfaction problems appear to undergo a “phase transition” from solubility to insolubility when the constraint density passes through a critical threshold. In all such cases it is easy to derive upper bounds on the location of the threshold by showing that abo ..."
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Cited by 41 (4 self)
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prove that the threshold for both random hypergraph 2colorability (Property B) and random NotAllEqual kSAT is 2 k−1 ln 2 − O(1). As a corollary, we establish that the threshold for random kSAT is of order Θ(2 k), resolving a longstanding open problem.
Results 1  10
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188,085