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split related work

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Boris Glavic 2020-12-19 08:32:58 -06:00
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main.tex
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\usepackage[normalem]{ulem}
\usepackage{subcaption}
\usepackage{booktabs}
\usepackage{todonotes}
\usepackage[disable]{todonotes}
\usepackage{graphicx}
\usepackage{listings}
%%%%%%%%%% SQL + proveannce listing settings
@ -191,6 +191,7 @@ sensitive=true
\appendix
\normalsize
\input{hardness-app}
\input{related-work-extra}
% \input{glossary.tex}
% \input{addproofappendix.tex}
\end{document}

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related-work-extra.tex Normal file
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Compressed Representations of Polynomials and Boolean Formulas}\label{sec:compr-repr-polyn}
There is a large body of work on compact using representations of Boolean formulas (e.g, various types of circuits including OBDDs~\cite{jha-12-pdwm}) and polynomials (e.g.,factorizations~\cite{OS16,DBLP:conf/tapp/Zavodny11}) some of which have been utilized for probabilistic query processing, e.g.,~\cite{jha-12-pdwm}. Compact representations of Boolean formulas for which probabilities can be computed in linear time include OBDDs, SDDs, d-DNNF, and FBDD. In terms of circuits over semiring expression,~\cite{DM14c} studies circuits for absorptive semirings while~\cite{S18a} studies circuits that include negation (expressed as the monus operation of a semiring). Algebraic Decision Diagrams~\cite{bahar-93-al} (ADDs) generalize BDDs to variables with more than two values. Chen et al.~\cite{chen-10-cswssr} introduced the generalized disjunctive normal form.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Parameterized Complexity}\label{sec:param-compl}
In~\Cref{sec:hard}, we utilized common conjectures from fine-grained complexity theory.
\BG{ATRI: Parameterized complexity discussion}

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related-work.tex
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\section{Related Work}\label{sec:related-work}
In addition to work on probabilistic databases, our work has connections to work on compact representations of polynomials and relies on past work in fine-grained complexity.
In addition to work on probabilistic databases, our work has connections to work on compact representations of polynomials and relies on past work in fine-grained complexity which we review in \Cref{sec:compr-repr-polyn} and \Cref{sec:param-compl}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Probabilistic Databases}\label{sec:prob-datab}
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Fink et al.~\cite{FH12} study aggregate queries over a probabilistic version of the extension of K-relations for aggregate queries proposed in~\cite{AD11d} (this data model is referred to as \emph{pvc-tables}). As an extension of K-relations, this approach supports bags. Probabilities are computed using a decomposition approach~\cite{DBLP:conf/icde/OlteanuHK10} over the symbolic expressions that are used as tuple annotations and values in pvc-tables. \cite{FH12} identifies a tractable class of queries involving aggregation. In contrast, we study a less general data model and query class, but provide a linear time approximation algorithm and provide new insights into the complexity of computing expectation (while \cite{FH12} computes probabilities for individual output annotations).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Compact Representations of Polynomials and Boolean Formulas}\label{sec:comp-repr-polyn}
There is a large body of work on compact using representations of Boolean formulas (e.g, various types of circuits including OBDDs~\cite{jha-12-pdwm}) and polynomials (e.g.,factorizations~\cite{OS16,DBLP:conf/tapp/Zavodny11}) some of which have been utilized for probabilistic query processing, e.g.,~\cite{jha-12-pdwm}. Compact representations of Boolean formulas for which probabilities can be computed in linear time include OBDDs, SDDs, d-DNNF, and FBDD. In terms of circuits over semiring expression,~\cite{DM14c} studies circuits for absorptive semirings while~\cite{S18a} studies circuits that include negation (expressed as the monus operation of a semiring). Algebraic Decision Diagrams~\cite{bahar-93-al} (ADDs) generalize BDDs to variables with more than two values. Chen et al.~\cite{chen-10-cswssr} introduced the generalized disjunctive normal form.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Parameterized Complexity Theory}\label{sec:param-compl-theory}
In~\Cref{sec:hard}, we utilized common conjectures from fine-grained complexity theory.
\BG{ATRI: Parameterized complexity discussion}
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