The Fanout Structure of Switching Functions

Hayes, John P.

doi:10.1145/321906.321918

Cited by 34 publications

(25 citation statements)

References 4 publications

(9 reference statements)

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“…DEFINITION 1 (Read-Once Function [17]). A Boolean formula φ is read-once if there exists a factorization such that each variable appears not more than once.…”

Section: Read-once Functions; Definitionsmentioning

confidence: 99%

“…It is well known that in probabilistic databases with independent tuples, every result tuple is associated with a Boolean formula [3,13] (often called lineage), and the query evaluation problem reduces to computing the marginal probabilities for the result tuple Boolean formulas holding true. Further, if a result tuple's Boolean formula can be factorized into a form where every Boolean variable appears at most once, also known as read-once functions [15,17], then the marginal probability can be computed easily in linear time. Hierarchical queries always admit a query evaluation plan such that the result tuple formulas are generated in read-once form, thus providing a connection to efficient query evaluation in probabilistic databases.…”

Section: Introductionmentioning

confidence: 99%

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Read-once functions and query evaluation in probabilistic databases

2010

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Probabilistic databases hold promise of being a viable means for large-scale uncertainty management, increasingly needed in a number of real world applications domains. However, query evaluation in probabilistic databases remains a computational challenge. Prior work on efficient exact query evaluation in probabilistic databases has largely concentrated on query-centric formulations (e.g., safe plans, hierarchical queries), in that, they only consider characteristics of the query and not the data in the database. It is easy to construct examples where a supposedly hard query run on an appropriate database gives rise to a tractable query evaluation problem. In this paper, we develop efficient query evaluation techniques that leverage characteristics of both the query and the data in the database. We focus on tuple-independent databases where the query evaluation problem is equivalent to computing marginal probabilities of Boolean formulas associated with the result tuples. Query evaluation is easy if the Boolean formulas can be factorized into a form that has every variable appearing at most once (called read-once); this suggests a naive approach that incorporates previously developed Boolean formula factorization algorithms into the query evaluation. We then develop novel, more efficient factorization algorithms that work for a large subclass of queries (specifically, conjunctive queries without self-joins), by exploiting the unique structure of the result tuple Boolean formulas. We empirically demonstrate that our proposed techniques are (1) orders of magnitude faster than generic inference algorithms when used to evaluate general read-once functions, and (2) for the special case of hierarchical queries, they rival the efficiency of prior techniques specifically designed to handle such queries.

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“…DEFINITION 1 (Read-Once Function [17]). A Boolean formula φ is read-once if there exists a factorization such that each variable appears not more than once.…”

Section: Read-once Functions; Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Read-once functions and query evaluation in probabilistic databases

2010

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show abstract

“…The above questions have been answered for more restricted sets of modules in the literature. Hayes [8], [9] answers questions 1) and 2) for AND, OR, and NOT, while Chakrabarti and Kolp [6] answer the same questions for arbitrary two input modules which is equivalent to considering AND, OR, NOT, and EXOR. Butler [5] gives counting formulas for functions of arbitrary two input modules.…”

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confidence: 99%

“…Hence, the function h = x G® X2 ® -.0-x. can be factored out ofvarious terms in (3) with the consequent decomposition f = g(h(xl, m xm), x.+ *--Xn,)* Hayes [8] has shown that a necessary and sufficient condition forfto have a decomposition of the form (2) with (3) where the summation operation is EXCLUSIVE-OR, ij's are either 0 or 1, such that i is the decimal equivalent of the binary number in" 2 il, and xij = 1 ifij = 0 and xii = xiif i = 1. Then where df/dx1 = df/dx2 = X3 X4.…”

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confidence: 99%