Finding Closest Point to a Set of Points (in Lat/Long)

Question

I am given a random set of points (not told how many) with a latitude and longitude and need to sort them.

I will then be given another random point (lat/long) and need to find the point closest to it (from the set above).

When I implement a linear search (put the set in a list and then calculate all the distances), it takes approximately 7 times longer than permitted.

So, I need a much more efficient sorting algorithm, but I am unsure how I could do this, especially since I'm given points that don't exist on a flat plane.

if you have a 3 dimensional one, and insert x,y,z coordinates, it will be using the chord length rather than the arc length, but should still give you the correct answer ? — Rusty Rob, Feb 03 '18 at 20:55
@SirGuy lat/long delta distances are not linearly proportional to their corresponding Euclidean distances — meowgoesthedog, Feb 04 '18 at 16:37
@meowgoesthedog Ah yes, I was thinking it was just for lookups because I didn't read the question correctly. — SirGuy, Feb 04 '18 at 18:58

score 1 · Answer 1 · answered Feb 12 '18 at 21:24

If your points are moderately well distributed then geometric hashing is a simple method to speed up nearest neighbor searches in practice. The idea is simply to register your objects in grid cells and do your search cell-wise so you can restrict your search to a local neighborhood.

This little python demo applied the idea to circles in the plane: Circles inserted into a geometric hash

So in your case you can choose some fixed N and split the longitude coordinates in [0, 2pi] into N equal parts and the latitude coordinates in [0, pi] into N parts. This gives you N^2 cells on the sphere. You register all your initial points at these cells.

When you are given the query point p then you start searching in the cell that is hit by p and in a large enough neighborhood such that you cannot miss the closest point.

If you initially register n points then you could choose N to something like sqrt(n)/4 or so.

Finding Closest Point to a Set of Points (in Lat/Long)

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