18 lines
1.5 KiB
TeX
18 lines
1.5 KiB
TeX
%root: main.tex
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%!TEX root=./main.tex
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\begin{abstract}
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In this work, we study the problem computing a tuple's expected multiplicity over bag-\abbrTIDB\xplural exactly and approximately.
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We refer to bag-\abbrTIDB\xplural as \abbrCTIDB\xplural, where $\bound$ is the bound on the maximum multiplicity. We are specifically
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interested in the fine-grained complexity and how it compares to the complexity of deterministic query evaluation algorithms --- if these complexities are comparable, it opens the door to practical deployment of probabilistic databases.
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Unfortunately, % we show the reverse;
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our results imply that computing expected multiplicities for \abbrCTIDB\xplural based on the results produced by such query evaluation algorithms introduces super-linear overhead (under parameterized complexity hardness assumptions/conjectures).
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We proceed to study approximation of expected multiplicities of result tuples of positive relational algebra queries ($\raPlus$) over \abbrCTIDB\xplural and for a non-trivial subclass of block-independent databases (\abbrBIDB\xplural).
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We develop a sampling algorithm that computes a $(1 \pm \epsilon)$-approximation of the expected multiplicity of an output tuple in time linear in the runtime of a comparable deterministic query for any $\raPlus$ query.
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% By removing Bag-PDB's reliance on the sum-of-products representation of polynomials, this result paves the way for future work on PDBs that are competitive with deterministic databases.
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\end{abstract}
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