6 research outputs found
Towards an Efficient Evaluation of General Queries
Database applications often require to
evaluate queries containing quantifiers or disjunctions,
e.g., for handling general integrity constraints. Existing
efficient methods for processing quantifiers depart from the
relational model as they rely on non-algebraic procedures.
Looking at quantified query evaluation from a new angle,
we propose an approach to process quantifiers that makes
use of relational algebra operators only. Our approach
performs in two phases. The first phase normalizes the
queries producing a canonical form. This form permits to
improve the translation into relational algebra performed
during the second phase. The improved translation relies
on a new operator - the complement-join - that generalizes
the set difference, on algebraic expressions of universal
quantifiers that avoid the expensive division operator in
many cases, and on a special processing of disjunctions by
means of constrained outer-joins. Our method achieves an
efficiency at least comparable with that of previous
proposals, better in most cases. Furthermore, it is considerably
simpler to implement as it completely relies on
relational data structures and operators
Rapid Sampling for Visualizations with Ordering Guarantees
Visualizations are frequently used as a means to understand trends and gather
insights from datasets, but often take a long time to generate. In this paper,
we focus on the problem of rapidly generating approximate visualizations while
preserving crucial visual proper- ties of interest to analysts. Our primary
focus will be on sampling algorithms that preserve the visual property of
ordering; our techniques will also apply to some other visual properties. For
instance, our algorithms can be used to generate an approximate visualization
of a bar chart very rapidly, where the comparisons between any two bars are
correct. We formally show that our sampling algorithms are generally applicable
and provably optimal in theory, in that they do not take more samples than
necessary to generate the visualizations with ordering guarantees. They also
work well in practice, correctly ordering output groups while taking orders of
magnitude fewer samples and much less time than conventional sampling schemes.Comment: Tech Report. 17 pages. Condensed version to appear in VLDB Vol. 8 No.
Randomized accuracy-aware program transformations for efficient approximate computations
Despite the fact that approximate computations have come to dominate many areas of computer science, the field of program transformations has focused almost exclusively on traditional semantics-preserving transformations that do not attempt to exploit the opportunity, available in many computations, to acceptably trade off accuracy for benefits such as increased performance and reduced resource consumption.
We present a model of computation for approximate computations and an algorithm for optimizing these computations. The algorithm works with two classes of transformations: substitution transformations (which select one of a number of available implementations for a given function, with each implementation offering a different combination of accuracy and resource consumption) and sampling transformations (which randomly discard some of the inputs to a given reduction). The algorithm produces a (1+ε) randomized approximation to the optimal randomized computation (which minimizes resource consumption subject to a probabilistic accuracy specification in the form of a maximum expected error or maximum error variance).National Science Foundation (U.S.). (Grant number CCF-0811397)National Science Foundation (U.S.). (Grant number CCF-0905244)National Science Foundation (U.S.). (Grant number CCF-0843915)National Science Foundation (U.S.). (Grant number CCF-1036241)National Science Foundation (U.S.). (Grant number IIS-0835652)United States. Dept. of Energy. (Grant Number DE-SC0005288)Alfred P. Sloan Foundation. Fellowshi