>On Mar 27, 2015 11:08 AM, "Dima Ivanovskiy" < dima...@mail.ru > wrote: >> >> Hello, I am Dmitrii, student of Moscow Institute of Physics and Technology >> >> Abstract: >> >> 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 >> https://www.pgcon.org/2011/schedule/attachments/197_pgcon-2011.pdf >> 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. >> >> >> Links: >> >> 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 >> >Nice proposal. >Dynamic Kdtrees can perform badly as the splitting median can get way off as >updates are coming. What are your thoughts about that? >Also what's up with the 4d space? I don't quite get it. These types are 2 or 3 >dimensions. I read spgist README one more time . I didn't find the mechanism for maintaining good balance after updates. I think we can use Bkd-Tree, https://www.cs.duke.edu/~pankaj/publications/papers/bkd-sstd.pdf . But It can be not the best solving. I include Research time in 2nd month of timeline.
About 4d space. All these types are 2 dimensional. Just as i n R-tree object is approximated by MBR. MBR for 2d-objects can be mapped to 4d-point. More general, nd-object MBR can be mapped into 2nd-point.