Question

Given a scenario where there are millions of potentially overlapping bounding boxes of variable sizes less the 5km in width.

Create a fast function with the arguments findIntersections(Longitude,Latitude,Radius) and the output is a list of those bounding boxes ids where each bounding box origin is inside the perimeter of the function argument dimensions.

How do I solve this problem elegantly?

Answer 1

This is normally done using an R-tree data structure

dbs like mysql or postgresql have GIS modules that use an r-tree under the hood to quickly retrieve locations within a certain proximity to a point on a map.

From http://en.wikipedia.org/wiki/R-tree:

R-trees are tree data structures that
are similar to B-trees, but are used
for spatial access methods, i.e., for
indexing multi-dimensional
information; for example, the (X, Y)
coordinates of geographical data. A
common real-world usage for an R-tree
might be: “Find all museums within 2
kilometres (1.2 mi) of my current
location”.

The data structure splits space with
hierarchically nested, and possibly
overlapping, minimum bounding
rectangles (MBRs, otherwise known as
bounding boxes, i.e. “rectangle”, what
the “R” in R-tree stands for).

The Priority R-Tree (PR-tree) is a variant that has a maximum running time of:

"O((N/B)^(1-1/d)+T/B) I/Os, where N is the number of d-dimensional (hyper-)
rectangles stored in the R-tree, B is the disk block size, and T is the output
size."

In practice most real-world queries will have a much quicker average case run time.

fyi, in addition to the other great code posted, there’s some cool stuff like SpatiaLite and SQLite R-tree module