golq : 2D Locality Queries
2D locality queries in Go
This utility is a spatial database which stores objects each of which is associated with a 2D point (a location in a 2D space). The points serve as the search key for the associated object. It is intended to efficiently answer circle inclusion queries, also known as range queries, basically questions like:
Which objects are within a radius R of the location L?
In this context, efficiently means significantly faster than the naive, brute force O(n) testing of all known points. Additionally it is assumed that the objects move along unpredictable paths, so that extensive preprocessing (for example, constructing a Delaunay triangulation of the point set) may not be practical.
The implementation is a bin lattice: a 2D rectangular array of brick-shaped (rectangles) regions of space. Each region is represented by a pointer to a (possibly empty) doubly-linked list of objects. All of these sub-bricks are the same size. All bricks are aligned with the global coordinate axes.
Usage example
TODO
Benchmarks
This logarithmic scale plot shows the numbers obtained in the following benchmarks. The brute-force method computes squared distances between every object and the randomly chosen search query point. It doesn't even include the additional time that would be taken to sort them in order to extract the nearest (or K nearest).
BenchmarkBruteForce10-2 2000000 819 ns/op
BenchmarkBruteForce50-2 500000 3570 ns/op
BenchmarkBruteForce100-2 200000 6958 ns/op
BenchmarkBruteForce200-2 100000 13564 ns/op
BenchmarkBruteForce500-2 50000 33037 ns/op
BenchmarkBruteForce1000-2 20000 66053 ns/op
BenchmarkNearestNeighbourLq10Radius2-2 3000000 546 ns/op
BenchmarkNearestNeighbourLq50Radius2-2 2000000 788 ns/op
BenchmarkNearestNeighbourLq100Radius2-2 1000000 1025 ns/op
BenchmarkNearestNeighbourLq200Radius2-2 1000000 1434 ns/op
BenchmarkNearestNeighbourLq500Radius2-2 500000 2431 ns/op
BenchmarkNearestNeighbourLq1000Radius2-2 300000 4242 ns/op
BenchmarkNearestNeighbourLq10Radius4-2 2000000 987 ns/op
BenchmarkNearestNeighbourLq50Radius4-2 1000000 1480 ns/op
BenchmarkNearestNeighbourLq100Radius4-2 1000000 1985 ns/op
BenchmarkNearestNeighbourLq200Radius4-2 500000 2974 ns/op
BenchmarkNearestNeighbourLq500Radius4-2 300000 5427 ns/op
BenchmarkNearestNeighbourLq1000Radius4-2 200000 9927 ns/op
BenchmarkObjectsInLocalityLq10Radius2-2 3000000 410 ns/op
BenchmarkObjectsInLocalityLq50Radius2-2 3000000 570 ns/op
BenchmarkObjectsInLocalityLq100Radius2-2 2000000 731 ns/op
BenchmarkObjectsInLocalityLq200Radius2-2 1000000 1051 ns/op
BenchmarkObjectsInLocalityLq500Radius2-2 1000000 1854 ns/op
BenchmarkObjectsInLocalityLq1000Radius2-2 500000 3418 ns/op
BenchmarkObjectsInLocalityLq10Radius4-2 2000000 808 ns/op
BenchmarkObjectsInLocalityLq50Radius4-2 1000000 1102 ns/op
BenchmarkObjectsInLocalityLq100Radius4-2 1000000 1440 ns/op
BenchmarkObjectsInLocalityLq200Radius4-2 1000000 2169 ns/op
BenchmarkObjectsInLocalityLq500Radius4-2 300000 4000 ns/op
BenchmarkObjectsInLocalityLq1000Radius4-2 200000 7881 ns/op
PASS
ok github.com/arl/golq 53.587s
Credits
This library is loosely inspired by the C language lq utility in OpenSteer.