\subsection{Problem definition}
\label{subsec:lmdk-sel-prob}

The problem setting is similar to the one that we described in detail in Section~\ref{subsec:lmdk-set}.
The main difference in this case lies in our threat model where we consider, in addition to the values of the regular and {\thething} events, the {\thething} timestamps $L$ privacy-sensitive as well.

Given a set of {\thethings} at respective timestamps $\{l_k\}$ in a series of events at $\{t_n\}$, such that $\{l_k\} \subseteq \{t_n\}$, a data publisher might release this information by:

\begin{enumerate}
  \item Selecting a set of options (Section~\ref{subsec:lmdk-set-opts}) consisting of different possible versions of $\{l_k\}$.
  
  \mk{`option' or `candidate'?}

  This could be:

  \begin{itemize}
    \item either a random set of $k$ other timestamps similar to the actual {\thething} timestamps (Section~\ref{subsec:lmdk-rnd}),
    \item or a set including $\{l_k\}$ and $x \in [1, n - k]$ additional dummy timestamps (Section~\ref{subsec:lmdk-dum-gen}).
  \end{itemize}

  \item Releasing a privacy-preserving version of the {\thething} timestamps (Section~\ref{subsec:priv-opt-sel}).
  We utilize the exponential mechanism with a utility function that calculates an indicator for each of the options in the set that we selected in the previous step.
  The utility depends on the positioning of the {\thething} timestamps of an option in the series, e.g.,~the distance from the previous/next {\thething}, the distance from the start/end of the series, etc.
\end{enumerate}

Following this process allows the release, and thereafter processing, of {\thething} timestamps.
Thus, we provide an extra layer of privacy protection when we separate {\thethings} from regular events.
