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+*.nav
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+*.out
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+*.snm
+*.toc
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+\documentclass[aspectratio=169]{beamer}
+
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage[english]{babel}
+
+\usetheme{metropolis}
+
+\title{Keys in Graphs}
+\author{Yohann D'Anello}
+\date{January, $31^{\text{st}}$ 2022}
+
+\begin{document}
+
+\begin{frame}
+\maketitle
+\end{frame}
+
+\begin{frame}{Project goal}
+This project aims to find Graph keys, as defined in
+\footnote{\url{https://www.researchgate.net/publication/283189709_Keys_for_graphs}}.
+A Graph Key describes the relations that an object can have with their keys, and
+what relations these involved objects can have.
+\end{frame}
+
+\begin{frame}{Graph key example}
+\begin{center}
+\begin{tikzpicture}[y=3cm]
+\node[draw] (0) at (0, 0) {Book};
+\node[] (00) at (-3, -1) {x};
+\node[draw] (01) at (-1, -1) {Person};
+\node[] (02) at (1, -1) {y};
+\node[draw] (03) at (3, -1) {Company};
+\node[draw] (010) at (-2, -2) {Country};
+\node[] (011) at (0, -2) {z};
+\node[] (030) at (3, -2) {t};
+\draw[->] (0) -- (00) node[midway,above,sloped] {title};
+\draw[->] (0) -- (01) node[midway,above,sloped] {author};
+\draw[->] (0) -- (02) node[midway,above,sloped] {subtitle};
+\draw[->] (0) -- (03) node[midway,above,sloped] {publisher};
+\draw[->] (01) -- (010) node[midway,above,sloped] {nationality};
+\draw[->] (01) -- (011) node[midway,above,sloped] {last name};
+\draw[->] (03) -- (030) node[midway,above,sloped] {identifier};
+\end{tikzpicture}
+\end{center}
+\end{frame}
+
+\begin{frame}{How generate keys?}
+To generate these keys, one suggests to find $n$-almost keys using SAKey,
+then to explore involved relations that define a domain and a range, and to
+explore recursively the related fields.
+
+  \begin{itemize}
+    \item Choose a dataset
+    \item Use \emph{SAKey} to find $n$-almost keys in the dataset
+    \item Find extracted relations that define a domain and a range
+    \item Explore recursively graph keys of discovered related items
+    \item Concatene these graphs
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Implementation}
+  \begin{itemize}
+    \item Simple script using Python 3.9+
+    \item Libraries: \emph{beautifulsoup4}, \emph{lxml} (ontology parsing),
+          \emph{SPARQLWrapper} (for SPARQL queries)
+    \item Uses the given binary for SAKey
+    \item Source code: \url{https://gitlab.crans.org/ynerant/graph-keys}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Algorithm}
+  \begin{itemize}
+    \item Input: class name $c$, threshold $n$, query limit $l$, recursivity limit $r$
+    \item Query DBPedia to get $l$ first rows of triples that describe the class $c$
+    \item Use \emph{SAKey} to find $n$-almost keys in the computed dataset of $l$ triples
+    \item Parse relations and filter those define a range
+    \item Process recursively on each discovered range with decrementing $r$, until $r$ is equal to $0$
+    \item Compute all given graphs
+    \item Display them
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Usage}
+  \texttt{./main.py Library 5 -{}-limit 3000 -{}-recursion 3}
+\end{frame}
+
+\begin{frame}{Difference with the given binary}
+  \begin{itemize}
+    \item Given material: linear
+    \item Given datasets: concern only one type of data, impossible to explore more with these triples
+    \item $\implies$ Choice to query DBPedia to get more data
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Discovered ranges}
+  \begin{itemize}
+    \item Example: we discovered that \texttt{[inCemetery, hasSize]} is a key for
+          \emph{GraveMonument}
+    \item Relation \texttt{inCemetery} has for domain \texttt{GraveMonument}
+          and for range \texttt{Cemetery}
+    \item We can now query data about cemeteries to get larger keys
+  \end{itemize}
+
+  \begin{center}
+    \begin{tikzpicture}[y=3cm]
+      \node[draw] (0) at (0, 0) {GraveMonument};
+      \node[draw] (1) at (-2, -1) {Cemetery};
+      \node (2) at (2, -1) {x};
+
+      \draw[->] (0) -- (1) node[midway,above,sloped] {inCemetery};
+      \draw[->] (0) -- (2) node[midway,above,sloped] {hasSize};
+    \end{tikzpicture}
+  \end{center}
+\end{frame}
+
+\begin{frame}{Output example}
+\begin{figure}[H]
+\centering
+\begin{tikzpicture}[x=3cm]
+\node[draw] (0) at (0, 0) {Library};
+\pause
+\node[draw] (0-0) at (1, 0) {Place};
+\draw[->] (0) -- (0-0) node[midway,above,sloped] {location};
+\pause
+\node[draw] (0-0-0) at (2, 0) {City};
+\draw[->] (0-0) -- (0-0-0) node[midway,above,sloped] {capital};
+\pause
+\node[draw] (0-0-0-0) at (3, 0) {Image};
+\draw[->] (0-0-0) -- (0-0-0-0) node[midway,above,sloped] {thumbnail};
+\end{tikzpicture}
+\caption{Sample output of the program}
+\end{figure}
+\end{frame}
+
+\begin{frame}{Limitations}
+  \begin{itemize}
+    \item Only few keys are well-typed (with a domain and/or a range)
+    \item We only extend minimal $n$-almost keys
+    \item We never generate minimal graph keys $\implies$ some keys could never be generated
+    \item Lot of paths
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Further works}
+  \begin{itemize}
+    \item Generate graphs with leaves (easy)
+    \item Explore triples of the form \texttt{?x ?r ?y} where we specify
+          the class of \texttt{?y} instead of \texttt{?x}
+    \item Explore relations that does not define any range (hard)
+    \item Take into account the \texttt{sameAs} relation
+    \item Find a way to generate more complex graphs
+  \end{itemize}
+\end{frame}
+
+\end{document}