40 lines
1.8 KiB
TeX
40 lines
1.8 KiB
TeX
%root: main.tex
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\section{Outline of 1st ICDT Introduction Submission}
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\begin{outline}[enumerate]
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\1 Problem Introduction and Background
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\2 Set-\abbrPDB notation, concepts, common (known) results
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\3 Dichotomy
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\3 Exact Computation \sharpphard
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\2 Formal definition of expected result multiplicity
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\2 Example
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\3 Assumed setting of {\emph set inputs}
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\3 Example based on explaining and motivating formal definition of expected result multiplicity
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\1 Discussion of set-\abbrPDB\xplural
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\2 Lineage from PosBool$[\vct{X}]$
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\2 Encoding of possible worlds via $\vct{X}$
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\2 Computing probability can be done using only the lineage
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\1 Discussion of bag-\abbrPDB\xplural
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\2 Link to $\domN[\vct{X}]$
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\2 Link to computing the expected count of a lineage polynomial
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\2 Example to illustrate computing an expected count over a lineage polynomial
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\1 Computing expected multiplicity for an \abbrSOP representation versus a factorized representation
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\2 Linear for \abbrSOP
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\2 Introduce the problem by asking if it's linear in the size of the representation for factorized representation produced by such query optimizations as projection push-down.
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\2 State our theoretical results (informally) that it is not linear in general
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\1 Contributions
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\2 Hardness results for the expected multiplicity problem
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\3 Reduction to counting $\kElem$-matchings
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\2 Introduce our approximation algorithm and its guarantees
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\2 Generalization to bag-\abbrPDB\xplural
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\2 Result over $\raPlus$ queries
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\2 Higher moments
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\1 Overview of our techniques
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\2 Informal introduction to $\rpoly$ with example
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\2 Definition of reduced polynomial
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\2 Equivalence of $\rpoly$ and computing $\expct$
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\2 Further details into the technique of obtaining our hardness result
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\1 Paper organization
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\2 Also includes evaluation semantics figure
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\end{outline} |