Organizing stuff
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		@ -22,7 +22,7 @@ To accompany and facilitate the descriptions in this chapter, we provide the fol
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  The `Status' attribute includes information that characterizes the user's state or the query itself, and its value varies according to the service functionality.
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  Subsequently, the generated data are aggregated (by issuing count queries over them) in order to derive useful information about the popularity of the venues during the day (Table~\ref{tab:snapshot-statistical}).
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  \includetable{snapshot}
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  \includetable{preliminaries/snapshot}
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\end{example}
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@ -43,7 +43,7 @@ Depending on the span of the observation, we distinguish the following categorie
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  The two data tables over the time-span $[t_1, t_2]$ are an example of finite data.
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  Infinite data are the whole series of data obtained over the period~$[t_1, \infty)$ (infinity is denoted by `\dots').
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  \includetable{continuous}
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  \includetable{preliminaries/continuous}
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\end{example}
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@ -69,10 +69,10 @@ We categorize data processing and publishing based on the implemented scheme \ka
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\begin{figure}[htp]
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  \centering
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  \subcaptionbox{Global scheme\label{fig:scheme-global}}{%
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    \includegraphics[width=\linewidth]{scheme-global}%
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    \includegraphics[width=\linewidth]{preliminaries/scheme-global}%
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  } \\ \bigskip
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  \subcaptionbox{Local scheme\label{fig:scheme-local}}{%
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   \includegraphics[width=\linewidth]{scheme-local}%
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   \includegraphics[width=\linewidth]{preliminaries/scheme-local}%
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  }
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  \caption{The usual flow of user-generated data, optionally harvested by data publishers, privacy-protected, and released to data consumers, according to the (a)~global, and (b)~local privacy schemes.}
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  \label{fig:privacy-schemes}
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@ -116,13 +116,13 @@ We identify two main data processing and publishing modes: \kat{but so far you h
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\begin{figure}[htp]
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  \centering
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  \subcaptionbox{Snapshot mode\label{fig:mode-snapshot}}{%
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    \includegraphics[width=.4\linewidth]{mode-snapshot}%
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    \includegraphics[width=.4\linewidth]{preliminaries/mode-snapshot}%
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  } \\ \bigskip\hspace{\fill}
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  \subcaptionbox{Batch mode\label{fig:mode-batch}}{%
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    \includegraphics[width=.4\linewidth]{mode-batch}%
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    \includegraphics[width=.4\linewidth]{preliminaries/mode-batch}%
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  }\hspace{\fill}
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  \subcaptionbox{Streaming mode\label{fig:mode-streaming}}{%
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    \includegraphics[width=.4\linewidth]{mode-streaming}%
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    \includegraphics[width=.4\linewidth]{preliminaries/mode-streaming}%
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  }\hspace{\fill}
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  \caption{The different data processing and publishing modes of continuously generated data sets.
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  (a)~Snapshot publishing, (b)~continuous publishing--batch mode, and (c)~continuous publishing--streaming mode.
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@ -99,13 +99,13 @@ Finally, in $2$-event-level (Figure~\ref{fig:level-w-event}) it is hard to deter
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\begin{figure}[htp]
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  \centering
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  \hspace{\fill}\subcaptionbox{Event-level\label{fig:level-event}}{%
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    \includegraphics[width=.32\linewidth]{level-event}%
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    \includegraphics[width=.32\linewidth]{preliminaries/level-event}%
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  }\hspace{\fill}
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  \subcaptionbox{User-level\label{fig:level-user}}{%
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    \includegraphics[width=.32\linewidth]{level-user}%
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    \includegraphics[width=.32\linewidth]{preliminaries/level-user}%
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  }\hspace{\fill}
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  \subcaptionbox{$2$-event-level\label{fig:level-w-event}}{%
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    \includegraphics[width=.32\linewidth]{level-w-event}%
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    \includegraphics[width=.32\linewidth]{preliminaries/level-w-event}%
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  }\hspace{\fill}
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  \caption{Protecting the data of Table~\ref{tab:continuous-statistical} on (a)~event-, (b)~user-, and (c)~$2$-event-level. A suitable distortion method can be applied accordingly. 
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  % \kat{Why don't you distort the results already in this table?}
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@ -301,7 +301,7 @@ A specialization of this mechanism for location data is the \emph{Planar Laplace
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\begin{figure}[htp]
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  \centering
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  \includegraphics[width=.7\linewidth]{laplace}
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  \includegraphics[width=.7\linewidth]{preliminaries/laplace}
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  \caption{A Laplace distribution for location $\mu = 2$ and scale $b = 1$.}
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  \label{fig:laplace}
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\end{figure}
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@ -436,7 +436,7 @@ Naturally, using the same (or different) privacy mechanism(s) multiple times to
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  Then, the reported data are collected by the central service, in order to be protected and then published, either as a whole, or as statistics thereof.
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  Notice that in order to showcase the straightforward application of $k$-anonymity and differential privacy, we apply the two methods on each timestamp independently from the previous one, and do not take into account any additional threats imposed by continuity.
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  \includetable{scenario-micro}
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  \includetable{preliminaries/scenario-micro}
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  First, we anonymize the data set of Table~\ref{tab:continuous-micro} using $k$-anonymity, with $k = 3$.
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  This means that any user should not be distinguished from at least $2$ others.
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@ -447,7 +447,7 @@ Naturally, using the same (or different) privacy mechanism(s) multiple times to
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  Finally, we achieve $3$-anonymity by putting the entries in groups of three, according to the quasi-identifiers.
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  Table~\ref{tab:scenario-micro} depicts the results at each timestamp.
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  \includetable{scenario-statistical}
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  \includetable{preliminaries/scenario-statistical}
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  Next, we demonstrate differential privacy.
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  We apply an $\varepsilon$-differentially private Laplace mechanism, with $\varepsilon = 1$, taking into account the count query that generated the true counts of Table~\ref{tab:continuous-statistical}.
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