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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. and points concentrated in specific inEach probability density will need the following properties: | 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. and points concentrated in specific inEach probability density will need the following properties: |
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. and points concentrated in specific inEach probability density will need the following properties:
- Parameters that define the distribution e.g.
- Center location
- Spatial size
- Standard deviation
- A measure of symmetry or skew
A multi-dimensional probability function preferably a function that uses types functions as parameters e.g. latex2(
)A theory to update, delete or insert points and the distributions based on changes to points.
Based on this last item, we must maintain a database of 4-dimensional points that we index using 4-dimensional, probability buckets.