Hello, I am Dmitrii, student of Moscow Institute of Physics and Technology

I chose project "Indexing prolonged geometrical objects (i.e. boxes, circles, 
polygons, not points) with SP-GiST by mapping to 4d-space". 
According to the presentation
SP-GIST 3 times faster than GiST in some cases. But GIST supports geometrical 
data types: 
box, circle, polygon with operators: && &> &< &<| >> << <<| <@ @> @ |&> |>> ~ ~=
Popular spatial extension PostGIS doesn't include SP-GIST, but has a lot of 
geometrical features.

Project details:
After meeting with Alexander Korotkov, I wrote some plan. 
Using of K-D-tree and Quadtree in building index for geometrical data types can 
increase speed of search in some cases.
The main idea is representing 2-D geometrical objects in their bounding box. 
Set of 2-D boxes is 4-D space. 
New _ops will work with points from 4-D space, for example kd_box_ops, 
quad_circle_ops and will support all geometrical operators. 
After conversion object to their bounding box algo has set of tuples (x1, y1, 
x2, y2). 
Our goal is separate this space the most equally. If we talk about K-D-tree, on 
first step K-D-tree algorithm will split space in 2 parts by the first 
coordinate, in next step by the second coordinate etc., after 4-th coordinate 
we repeat this procedure. 
At the end we have index at geometrical objects and use traversal tree for 
every search operator. 

Postgresql has already has realization ideas of MBR in gist/gistproc.c. So I 
will transfer this realization to other type of tree.

Of cource, I assume that SP-GIST can be not the best decision of this problem. 
So after testing this clear methods, I will try to find more effective way. 
Maybe with using combination of different spatial tree structures.

Project Schedule:

until May 25

Read documentation and source code, clarify details of implementation.

1st month

Implement new '_ops' with all geometrical operators for box, circle, polygon

2nd month

Research new methods for increase speed of geometrical query

3rd month

Final refactoring, testing and submitting a patch.

http://www.sai.msu.su/~megera/postgres/talks/gist_tutorial.html - about GIST
https://toster.ru/q/27135#answer_110197 - people need SP-GIST for cubes
http://www.slideshare.net/profyclub_ru/o-lt - presentation about indexes
http://pgconf.ru/static/presentations/2015/korotkov_spatial.pdf - working with 
geo objects

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