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

Merge branch 'master' of gitlab.odin.cse.buffalo.edu:ahuber/SketchingWorlds

Browse source
This commit is contained in:
Oliver Kennedy 2020-06-26 17:28:07 -04:00
parent 0d58ec08b7 79903caaa3
commit 767f3676bf
Signed by: okennedy
GPG key ID: 3E5F9B3ABD3FDB60
2 changed files with 8 additions and 5 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

3
poly-form.tex
View file

@ -84,6 +84,7 @@ We would like to argue that in the general case there is no computation of expec
To this end, consider the following graph $G(V, E)$, where $|E| = m$, $|V| = \numTup$, and $i, j \in [\numTup]$. Consider the query $q_E(X_1,\ldots, X_\numTup) = \sum\limits_{(i, j) \in E} X_i \cdot X_j$.
\AR{The two lemmas need to be re-written once notation for representing a query is finalized in Section 1.}
\AH{\^-----This is an issue that we are currently discussing.}
\begin{Lemma}\label{lem:const-p}
If we can compute $\poly(\wElem_1,\ldots, \wElem_\numTup) = q_E(\wElem_1,\ldots, \wElem_\numTup)^3$ in T(m) time for $\wElem_1 = \ldots = \wElem_\numTup = \prob$, then we can count the number of 3-matchings in $G$ in $T(m) + O(m)$ time.
\end{Lemma}
@ -189,3 +190,5 @@ Then $\numocc{\tri}_2 = 0$, and if we can prove that\AR{Again you are not transc
\end{itemize}
we solve our problem for $q_E^3$ based on $G_2$ and we can compute $\numocc{\threedis}$, a hard problem.
\end{proof}
{\bf TESTING}
$\vec{w}\sim\mathcal{D}$

10
ra-to-poly.tex
View file

@ -2,11 +2,11 @@
%!TEX root=./main.tex
\section{Query translation into polynomials}
\AH{This section will involve the set of queries (RA+) that we are interested in, the probabilistic/incomplete models we address, and the outer aggregate functions we perform over the output \textit{annotation}
1) RA notation
2) DB (TIDB) notation
3) How queries translate into polynomials
}
%\AH{This section will involve the set of queries (RA+) that we are interested in, the probabilistic/incomplete models we address, and the outer aggregate functions we perform over the output \textit{annotation}
%1) RA notation
%2) DB (TIDB) notation
%3) How queries translate into polynomials
%}
Given tables $\rel, \reli$, an arbitrary query $\query(\rel)$ over the positive relational operators (SPJU), abusing notation slightly denote the query polynomial as $\poly(X_1,\ldots, X_\numTup)$.
\OK{