From 049b21019385667b4b851cbd547cabcd9674b57e Mon Sep 17 00:00:00 2001
From: Aaron Huber <ahuber@buffalo.edu>
Date: Thu, 19 Nov 2020 11:04:04 -0500
Subject: [PATCH] Added Paper Outline.

---
 intro.tex | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

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}
+
 
 
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