From 262debf68ccaf0e797a208e5c24581157352d267 Mon Sep 17 00:00:00 2001 From: Aaron Huber Date: Thu, 8 Apr 2021 15:42:29 -0400 Subject: [PATCH] Small changes to S6 and S7 (Aaron) --- related-work.tex | 15 ++++----------- 1 file changed, 4 insertions(+), 11 deletions(-) diff --git a/related-work.tex b/related-work.tex index 87c8a6f..740e323 100644 --- a/related-work.tex +++ b/related-work.tex @@ -5,25 +5,18 @@ %\subsection{Probabilistic Databases}\label{sec:prob-datab} \textbf{Probabilistic Databases} (PDBs) have been studied predominantly for set semantics. Many data models have been proposed for encoding PDBs more compactly than as sets of possible worlds. -These include tuple-independent databases~\cite{VS17} (\tis), block-independent databases (\bis)~\cite{RS07}, and \emph{PC-tables}~\cite{GT06} pair a C-table % ~\cite{IL84a} -with probability distribution over its variables. -This is similar to our $\semNX$-PDBs, with Boolean expressions instead of polynomials. -% Tuple-independent databases (\tis) consist of a classical database where each tuple associated with a probability and tuples are treated as independent probabilistic events. -% While unable to encode correlations directly, \tis are popular because any finite probabilistic database can be encoded as a \ti and a set of constraints that ``condition'' the \ti~\cite{VS17}. -% Block-independent databases (\bis) generalize \tis by partitioning the input into blocks of disjoint tuples, where blocks are independent~\cite{RS07}. %,BS06 -% \emph{PC-tables}~\cite{GT06} pair a C-table % ~\cite{IL84a} -% with probability distribution over its variables. This is similar to our $\semNX$-PDBs, except that we do not allow for variables as attribute values and instead of local conditions (propositional formulas that may contain comparisons), we associate tuples with polynomials $\semNX$. +These include tuple-independent databases~\cite{VS17} (\tis), block-independent databases (\bis)~\cite{RS07}, and \emph{PC-tables}~\cite{GT06}, which is similar to our $\semNX$-PDBs, with Boolean expressions instead of polynomials. Approaches for probabilistic query processing (i.e., computing marginal probabilities for tuples), fall into two broad categories. -\emph{Intensional} (or \emph{grounded}) query evaluation computes the \emph{lineage} of a tuple % (a Boolean formula encoding the provenance of the tuple) +\emph{Intensional} (or \emph{grounded}) query evaluation computes the \emph{lineage} of a tuple and then the probability of the lineage formula. In this paper we focus on intensional query evaluation with polynomials. It has been shown that computing the marginal probability of a tuple is \sharpphard~\cite{valiant-79-cenrp} (by reduction from weighted model counting). The second category, \emph{extensional} query evaluation, % avoids calculating the lineage. % This approach is in \ptime, but is limited to certain classes of queries. -Dalvi et al.~\cite{DS12} proved a dichotomy for unions of conjunctive queries (UCQs): -for any UCQ the probabilistic query evaluation problem is either \sharpphard (requires extensional evaluation) or \ptime (permits intensional). +Dalvi et al.~\cite{DS12} proved a dichotomy for UCQs: +for any UCQ the probabilistic query evaluation problem is either \sharpphard or \ptime. Olteanu et al.~\cite{FO16} presented dichotomies for two classes of queries with negation. % R\'e et al~\cite{RS09b} present a trichotomy for HAVING queries. Amarilli et al. investigated tractable classes of databases for more complex queries~\cite{AB15}. %,AB15c Another line of work, studies which structural properties of lineage formulas lead to tractable cases~\cite{kenig-13-nclexpdc,roy-11-f,sen-10-ronfqevpd}.