Diff for "DynamicMaxCount"

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\section{Dynamic Max Count}

This contains the ideas and notes for a Dynamic Max Count (Dynamic Max-in-time) aggregate operator

\subsection{Concept}

Instead of using Hyper-buckets that have discrete boundaries and densities which can not be updated reasonably using the MaxCountProgramNotes ideas, we propose a probabilistic method where by we put probability densities in space. Each probability density will need the following properties:

\begin{enumerate}

• \item Parameters that define the distribution e.g. \begin{enumerate}
  • \item Center location \item Spatial size \item Standard deviation \item A measure of symmetry or skew
  \end{enumerate} \item A multi-dimensional probability function preferably a function that uses types functions as parameters e.g. $p(x_u(t),x_l(t),y_u(t),y_l(t)[,z_u(t),z_l(t)])$ \item A theory to update ({\em delete} or {\em insert} points) the distributions based on changes to points.

\end{enumerate}

Based on this last item, we must maintain a database of 4-dimensional points that we index using 4-dimensional, probability buckets.

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