Results 1  10
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1,863,590
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 766 (5 self)
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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 NP
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 793 (39 self)
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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
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 475 (67 self)
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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
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 409 (21 self)
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We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than
Some optimal inapproximability results
, 2002
"... We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for ..."
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Cited by 748 (11 self)
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for the efficient approximability of many optimization problems studied previously. In particular, for MaxE2Sat, MaxCut, MaxdiCut, and Vertex cover. Warning: Essentially this paper has been published in JACM and is subject to copyright restrictions. In particular it is for personal use only.
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 792 (27 self)
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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
A Survey of Approaches to Automatic Schema Matching
 VLDB JOURNAL
, 2001
"... Schema matching is a basic problem in many database application domains, such as data integration, Ebusiness, data warehousing, and semantic query processing. In current implementations, schema matching is typically performed manually, which has significant limitations. On the other hand, previous ..."
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Cited by 1328 (51 self)
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level and instancelevel, elementlevel and structurelevel, and languagebased and constraintbased matchers. Based on our classification we review some previous match implementations thereby indicating which part of the solution space they cover. We intend our taxonomy and review of past work to be useful when
Stable Signal Recovery from Incomplete and Inaccurate Measurements
, 2006
"... Suppose we wish to recover a vector x0 ∈ Rm (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x0 accurately based on the data y? To recover x0, we ..."
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Cited by 1363 (38 self)
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, we consider the solution x to the 1regularization problem min ‖x‖1 subject to ‖Ax − y‖2 ≤ , where is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the vector x0 is sufficiently sparse, then the solution is within the noise
PComplete Approximation Problems
, 1976
"... For Pcomplete problems such as traveling salesperson, cycle covers, 01 integer programming, multicommodity network flows, quadratic assignment, etc, it is shown that the approximation problem is also Pcomplete In contrast with these results, a linear time approximation algorithm for the clusterin ..."
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Cited by 366 (0 self)
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For Pcomplete problems such as traveling salesperson, cycle covers, 01 integer programming, multicommodity network flows, quadratic assignment, etc, it is shown that the approximation problem is also Pcomplete In contrast with these results, a linear time approximation algorithm
Results 1  10
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1,863,590