Dynamic Max Count

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

Concept

Instead of using Hyper-buckets that have constant densities which can not be updated reasonably using the MaxCountProgramNotes ideas, we propose a probabilistic method where by we define a probability density function in each hyper-bucket. In a sense we are not trying to minimize skew in the bucket creation process, but recognizing and modeling skew in each bucket. The added advantage to this concept is that a region equivalent to a hyper-bucket containing no points may be excluded from the index. Consequently the algorithm searches a smaller space. For example if it becomes necessary to shrink the size of a hyper-bucket to latex2($10~unit^{6}$) size in a latex2($10000~unit^6$) space we will have latex2($1 \times 10^{18}$) buckets. With points concentrated in specific regions we will only have to track a fraction of these in the index.

Here is a description of the index:

1. Index defines
   1. Spatial dimensions
   2. Bucket Dimensions
   3. Histogram divisions that determine the level of approximation in each hyper-bucket (see below)

   4. A multi-dimensional probability function preferably a function that uses functions as parameters e.g. latex2($p(x_u(t),x_l(t),y_u(t),y_l(t)[,z_u(t),z_l(t)])$)

2. A theory to update, delete or insert points and the distributions based on changes to points.

The above has been implemented in C# 8/15/2005.

Thus we maintain a database of 4-dimensional points that we index using 6-dimensional, probability buckets.