[postgis-devel] Project Proposal GSOC16 | SFCs

[Ankush Chauhan]

Hi Brian Hamlin,
In continuation to our IRC chats, I want to present an approach of implementing space filling curves for mapping 2D space to linear data which can be indexed using current R-Tree-over-GiST scheme in PostGIS. #3
So the basic idea is to extend the current GIST scheme which may allow PostGIS users to map using SFC’s namely the Hilbert, Serpenski and Moore Curves, which have the potential to enhance scalability of PostGIS based SDBs.

Real world utility will include choosing the right spatial indexing mechanism based upon certain application requirements, for instance application requiring secondary disk accesses may try to reduce jump segments, whereas for primary memory accesses a jump segment could be highly favorable. Moreover, the directional segments may help determine the flow of SFC growth and also using the total directional vector.  #1

All of these algorithms are continuous recursive fractal curve generators so the mapping an be from ∞ → N, which essentially means the mapping is never ending with increasing granularity.

·       For all recursive algorithms the number of hits per block remained constant with the increasing size of grid after grid size 16.

·       Number of disk blocks retrieved on a selection is a function only of the size of the selected set and not the size of the database.

·       For the specific class of queries studied, better than the worst case O(N^(k-1/k)) for k attribute selection on a database with N records. #2


References:

  1.  Mokbel, M.F., Aref, W.G. and Kamel, I., 2003. Analysis of multi-dimensional space-filling curves. GeoInformatica, 7(3), pp.179-209.
  2.  Moon, B., Jagadish, H.V., Faloutsos, C. and Saltz, J.H., 2001. Analysis of the clustering properties of the Hilbert space-filling curve. Knowledge and Data Engineering, IEEE Transactions on, 13(1), pp.124-141.
  3.  Obe, R.O. and Hsu, L.S., 2015. PostGIS in action. Manning Publications Co..

Regards
Ankush Chauhan
Student
Department of Computer Science
Georgia State University
Atlanta, GA
USA
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