diff --git a/intro.tex b/intro.tex index 8ac963b..04e4d43 100644 --- a/intro.tex +++ b/intro.tex @@ -57,6 +57,35 @@ of the algorithm is the output polynomial of the query as opposed to the input D in the size of the output polynomial rather than the input DB of the query, a polynomial that might be greater or lesser than the input depending on the structure of the query. +\section{Outline of the rest of the paper} +\begin{enumerate} + \item Background Knowledge and Notation + \begin{enumerate} + \item Review notation for PDBs + \item Review the use of semirings as generating output polynomials + \item Review the translation of semiring operators to RA operators + \item Polynomial formulation and notation + \end{enumerate} + \item Reduction to hardness results in graph theory + \begin{enumerate} + \item $\rpoly$ and its equivalence to $\expct\pbox{\poly}$ when $\vct{X} \in \{0, 1\}^\numvar$ + \item Results for SOP polynomial + \item Results for compressed version of polynomial + \item ~\cref{lem:const-p} proof + \end{enumerate} + \item Approximation Algorithm + \begin{enumerate} + \item Description of the Algorithm + \item Theoretical guarantees + \item Will we have time to tackle BIDB? + \begin{enumerate} + \item If so, experiments on BIDBs? + \end{enumerate} + \end{enumerate} + \item Future Work + \item Conclusion +\end{enumerate} + %%% Local Variables: