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145
Efficient Query Evaluation on Probabilistic Databases
, 2004
"... We describe a system that supports arbitrarily complex SQL queries with ”uncertain” predicates. The query semantics is based on a probabilistic model and the results are ranked, much like in Information Retrieval. Our main focus is efficient query evaluation, a problem that has not received attentio ..."
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Cited by 456 (47 self)
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We describe a system that supports arbitrarily complex SQL queries with ”uncertain” predicates. The query semantics is based on a probabilistic model and the results are ranked, much like in Information Retrieval. Our main focus is efficient query evaluation, a problem that has not received attention in the past. We describe an optimization algorithm that can compute efficiently most queries. We show, however, that the data complexity of some queries is #Pcomplete, which implies that these queries do not admit any efficient evaluation methods. For these queries we describe both an approximation algorithm and a MonteCarlo simulation algorithm.
A PolynomialTime Approximation Algorithm for the Permanent of a Matrix with NonNegative Entries
 JOURNAL OF THE ACM
, 2004
"... We present a polynomialtime randomized algorithm for estimating the permanent of an arbitrary n ×n matrix with nonnegative entries. This algorithm—technically a “fullypolynomial randomized approximation scheme”—computes an approximation that is, with high probability, within arbitrarily small spec ..."
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Cited by 427 (27 self)
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We present a polynomialtime randomized algorithm for estimating the permanent of an arbitrary n ×n matrix with nonnegative entries. This algorithm—technically a “fullypolynomial randomized approximation scheme”—computes an approximation that is, with high probability, within arbitrarily small specified relative error of the true value of the permanent.
Approximating the permanent
 SIAM J. Computing
, 1989
"... Abstract. A randomised approximation scheme for the permanent of a 01 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the ..."
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Cited by 345 (26 self)
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Abstract. A randomised approximation scheme for the permanent of a 01 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the graph. For a wide class of 01 matrices the approximation scheme is fullypolynomial, i.e., runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output. This class includes all dense matrices (those that contain sufficiently many l’s) and almost all sparse matrices in some reasonable probabilistic model for 01 matrices of given density. For the approach sketched above to be computationally efficient, the Markov chain must be rapidly mixing: informally, it must converge in a short time to its stationary distribution. A major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing, apparently the first such result for a Markov chain with genuinely complex structure. The techniques used seem to have general applicability, and are applied again in the paper to validate a fullypolynomial randomised approximation scheme for the partition function of an arbitrary monomerdimer system.
Approximate counting, uniform generation and rapidly mixing markov chains
 Inf. Comput
, 1989
"... The paper studies effective approximate solutions to combinatorial counting and uniform generation problems. Using a technique based on the simulation of ergodic Markov chains, it is shown that, for selfreducible structures, almost uniform generation is possible in polynomial time provided only tha ..."
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Cited by 317 (11 self)
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The paper studies effective approximate solutions to combinatorial counting and uniform generation problems. Using a technique based on the simulation of ergodic Markov chains, it is shown that, for selfreducible structures, almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary polynomial factor is possible in polynomial time. It follows that, for selfreducible structures, polynomial time randomised algorithms for counting to within factors of the form (1
ULDBs: Databases with uncertainty and lineage
 IN VLDB
, 2006
"... This paper introduces ULDBs, an extension of relational databases with simple yet expressive constructs for representing and manipulating both lineage and uncertainty. Uncertain data and data lineage are two important areas of data management that have been considered extensively in isolation, howev ..."
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Cited by 310 (32 self)
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This paper introduces ULDBs, an extension of relational databases with simple yet expressive constructs for representing and manipulating both lineage and uncertainty. Uncertain data and data lineage are two important areas of data management that have been considered extensively in isolation, however many applications require the features in tandem. Fundamentally, lineage enables simple and consistent representation of uncertain data, it correlates uncertainty in query results with uncertainty in the input data, and query processing with lineage and uncertainty together presents computational benefits over treating them separately. We show that the ULDB representation is complete, and that it permits straightforward implementation of many relational operations. We define two notions of ULDB minimality—dataminimal and lineageminimal—and study minimization of ULDB representations under both notions. With lineage, derived relations are no longer selfcontained: their uncertainty depends on uncertainty in the base data. We provide an algorithm for the new operation of extracting a database subset in the presence of interconnected uncertainty. Finally, we show how ULDBs enable a new approach to query processing in probabilistic databases. ULDBs form the basis of the Trio system under development at Stanford.
Hardness vs. randomness
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1994
"... We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function tha ..."
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Cited by 298 (27 self)
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We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function that is hard for C. This construction reveals an equivalence between the problem of proving lower bounds and the problem of generating good pseudorandom sequences. Our construction has many consequences. The most direct one is that efficient deterministic simulation of randomized algorithms is possible under much weaker assumptions than previously known. The efficiency of the simulations depends on the strength of the assumptions, and may achieve P =BPP. We believe that our results are very strong evidence that the gap between randomized and deterministic complexity is not large. Using the known lower bounds for constant depth circuits, our construction yields an unconditionally proven pseudorandom generator for constant depth circuits. As an application of this generator we characterize the power of NP with a random oracle.
On the Hardness of Approximate Reasoning
, 1996
"... Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider va ..."
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Cited by 289 (13 self)
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Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge compilation, that use approximation to avoid computational difficulties, and reduce them to modelcounting problems over a propositional domain. We prove that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited. This should be contrasted with the case of deductive reasoning, where Horn theories and theories with binary clauses are distinguished by the e...
The Markov chain Monte Carlo method: an approach to approximate counting and integration. in Approximation Algorithms for NPhard Problems, D.S.Hochbaum ed
, 1996
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The NPcompleteness column: an ongoing guide
 JOURNAL OF ALGORITHMS
, 1987
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NPCompleteness," W. H. Freem ..."
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Cited by 239 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NPCompleteness," W. H. Freeman & Co., New York, 1979 (hereinafter referred to as "[G&J]"; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Efficient topk query evaluation on probabilistic data
 in ICDE
, 2007
"... Modern enterprise applications are forced to deal with unreliable, inconsistent and imprecise information. Probabilistic databases can model such data naturally, but SQL query evaluation on probabilistic databases is difficult: previous approaches have either restricted the SQL queries, or computed ..."
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Cited by 182 (32 self)
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Modern enterprise applications are forced to deal with unreliable, inconsistent and imprecise information. Probabilistic databases can model such data naturally, but SQL query evaluation on probabilistic databases is difficult: previous approaches have either restricted the SQL queries, or computed approximate probabilities, or did not scale, and it was shown recently that precise query evaluation is theoretically hard. In this paper we describe a novel approach, which computes and ranks efficiently the topk answers to a SQL query on a probabilistic database. The restriction to topk answers is natural, since imprecisions in the data often lead to a large number of answers of low quality, and users are interested only in the answers with the highest probabilities. The idea in our algorithm is to run in parallel several MonteCarlo simulations, one for each candidate answer, and approximate each probability only to the extent needed to compute correctly the topk answers. The algorithms is in a certain sense provably optimal and scales to large databases: we have measured running times of 5 to 50 seconds for complex SQL queries over a large database (10M tuples of which 6M probabilistic). Additional contributions of the paper include several optimization techniques, and a simple data model for probabilistic data that achieves completeness by using SQL views. 1