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122,508
The NonApproximability of NonBoolean Predicates
 Trevisan (Eds.), Proceedings of 5th International Workshop on Randomization and Approximation Techniques in Computer Science
, 2001
"... Constraint satisfaction programs where each constraint depends on a constant number of variables have the following property: The randomized algorithm that guesses an assignment uniformly at random satisfies an expected constant fraction of the constraints. By combining constructions from interactiv ..."
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Cited by 9 (2 self)
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Constraint satisfaction programs where each constraint depends on a constant number of variables have the following property: The randomized algorithm that guesses an assignment uniformly at random satisfies an expected constant fraction of the constraints. By combining constructions from interactive proof systems with harmonic analysis over finite groups, Hstad showed that for several constraint satisfaction programs this naive algorithm is essentially the best possible unless P = NP.
Approximation Algorithm for NonBoolean MAX kCSP
"... Abstract. In this paper, we present a randomized polynomialtime approximation algorithm for MAX kCSPd. In MAX kCSPd, we are given a set of predicates of arity k over an alphabet of size d. Our goal is to find an assignment that maximizes the number of satisfied constraints. Our algorithm has appr ..."
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Cited by 1 (0 self)
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approximation factor Ω(kd/d k) (when k ≥ Ω(log d)). This bound is asymptotically optimal assuming the Unique Games Conjecture. The best previously known algorithm has approximation factor Ω(k log d/d k). We also give an approximation algorithm for the boolean MAX kCSP2 problem with a slightly improved
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
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Cited by 855 (12 self)
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, it turns out that the numbers F0, F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k ≥ 6 requires nΩ(1) space. Applications to data bases are mentioned as well.
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae w.r.t the vertex set). Our graph property testing algorithms are probabilistic and make assertions which are correct with high probability, utilizing only poly(1=ffl) edgequeries into the graph, where ffl is the distance parameter. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph which corre...
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Lower Bounds for nonBoolean Constraint Satisfaction Programs
, 2000
"... . We show that the kCSP problem over a nite Abelian group G cannot be approximated within jGj k O( p k) , for any constant > 0, unless P = NP. This lower bound matches well with the best known upper bound, jGj k 1 , of Serna, Trevisan and Xhafa. The proof uses a combination of PCP tech ..."
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Cited by 2 (0 self)
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. We show that the kCSP problem over a nite Abelian group G cannot be approximated within jGj k O( p k) , for any constant > 0, unless P = NP. This lower bound matches well with the best known upper bound, jGj k 1 , of Serna, Trevisan and Xhafa. The proof uses a combination of PCP
Systematic design of program analysis frameworks
 In 6th POPL
, 1979
"... Semantic analysis of programs is essential in optimizing compilers and program verification systems. It encompasses data flow analysis, data type determination, generation of approximate invariant ..."
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Cited by 771 (52 self)
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Semantic analysis of programs is essential in optimizing compilers and program verification systems. It encompasses data flow analysis, data type determination, generation of approximate invariant
The (Parallel) Approximability of NonBoolean Satisfiability Problems and Restricted Integer Programming
 In Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
, 1997
"... We present parallel approximation algorithms for maximization problems expressible by integer linear programs of a restricted syntactic form introduced by Barland et al. [BKT96]. One of our motivations was to show whether the approximation results in the framework of Barland et al. holds in the para ..."
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Cited by 9 (0 self)
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over multivalued domains (which is a natural generalization of boolean constraint satisfaction and has additional relations to other problems), for which we show nonapproximability results and develop parallel approximation algorithms. Our parallel approximation algorithms are based on linear
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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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.
DecisionTheoretic Planning: Structural Assumptions and Computational Leverage
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1999
"... Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives ..."
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Cited by 510 (4 self)
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related methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies
Results 1  10
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122,508