http://vadimtropashko.wordpress.com/2008/07/12/matrix-encoding-growth/ with occasional pedestrian SQL topics Sun, 01 Nov 2009 17:24:11 +0000 http://wordpress.com/ hourly 1 http://vadimtropashko.wordpress.com/2008/07/12/matrix-encoding-growth/#comment-788 Yuriy Fuksenko Tue, 15 Jul 2008 20:44:08 +0000 http://vadimtropashko.wordpress.com/?p=71#comment-788 So, the biggest limitation at this point from my point of view is that as you going down the hierarchy and/or to the right through siblings, you can have less and less children. Here is an example: If you have a tree such that root has 2 children, and then second child has 3 children, and that 3rd child has 4 children, and 4th child has 5 children, and so on bottom right child on level 20 will not be able to get any children. So, the biggest limitation at this point from my point of view is that as you going down the hierarchy and/or to the right through siblings, you can have less and less children.
Here is an example:
If you have a tree such that root has 2 children, and then second child has 3 children, and that 3rd child has 4 children, and 4th child has 5 children, and so on bottom right child on level 20 will not be able to get any children.

]]> http://vadimtropashko.wordpress.com/2008/07/12/matrix-encoding-growth/#comment-786 Yuriy Fuksenko Mon, 14 Jul 2008 17:09:45 +0000 http://vadimtropashko.wordpress.com/?p=71#comment-786 If we use 64 bit integers, only a11 and a21 are unique, that gives us (2^64)^2. Because we have to use multiplication, in becames just 2^64. Sign takes away 1 bit, so it is 2^63. Now, if you look at node selected as root in the book,(a11=2;a21=1;a12=1;a22=0); you will see that it only covers interval from 1 to 2, and that will give you a very small subset of 2^63 posibilities. If instead you create a root that covers everything from 0 to infinity, it will look like a11=1;a21=0;a12=1;a22=-1; First level children than will look like (a11=n;a12=1;a21=1;a22=0),where n > 0. That makes the root described in the book just one of the children. Each child covers an interval of 1, with boundaries n-1,n. now, what I am worried about, is that it seems like for each next sibling you can have smaller amount of children. for example, if you take the last possible first level child [N,1,1,0], where N is Max possible number, you will not be able to add children to it. If we use 64 bit integers, only a11 and a21 are unique, that gives us (2^64)^2. Because we have to use multiplication, in becames just 2^64. Sign takes away 1 bit, so it is 2^63.
Now, if you look at node selected as root in the book,(a11=2;a21=1;a12=1;a22=0); you will see that it only covers interval from 1 to 2, and that will give you a very small subset of 2^63 posibilities.
If instead you create a root that covers everything from 0 to infinity, it will look like a11=1;a21=0;a12=1;a22=-1;
First level children than will look like (a11=n;a12=1;a21=1;a22=0),where n > 0. That makes the root described in the book just one of the children. Each child covers an interval of 1, with boundaries n-1,n.
now, what I am worried about, is that it seems like for each next sibling you can have smaller amount of children.
for example, if you take the last possible first level child [N,1,1,0], where N is Max possible number, you will not be able to add children to it.

]]>