ODIn/paper-BagRelationalPDBsAreHard
1
0
Fork 0
Code Issues Pull requests Projects Releases Wiki Activity

Small changes to S6 and S7 (Aaron)

Browse source
This commit is contained in:
Aaron Huber 2021-04-08 15:42:29 -04:00
parent c57cf0e973
commit 262debf68c
1 changed files with 4 additions and 11 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

15
related-work.tex
View file

@ -5,25 +5,18 @@
%\subsection{Probabilistic Databases}\label{sec:prob-datab} %\subsection{Probabilistic Databases}\label{sec:prob-datab}
\textbf{Probabilistic Databases} (PDBs) have been studied predominantly for set semantics. \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. 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} 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.
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 $\semNX$.
Approaches for probabilistic query processing (i.e., computing marginal probabilities for tuples), fall into two broad categories. 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. and then the probability of the lineage formula.
In this paper we focus on intensional query evaluation with polynomials. 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). 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. The second category, \emph{extensional} query evaluation, % avoids calculating the lineage.
% This approach % This approach
is in \ptime, but is limited to certain classes of queries. 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): Dalvi et al.~\cite{DS12} proved a dichotomy for UCQs:
for any UCQ the probabilistic query evaluation problem is either \sharpphard (requires extensional evaluation) or \ptime (permits intensional). 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. 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 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}. 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}.