Algorithm for finding nearby points?

Question

Given a set of several million points with x,y coordinates, what is the algorithm of choice for quickly finding the top 1000 nearest points from a location? \"Quickly\" here mea

Answer 1

I assume the points are in a database or some searchable indexed location? If so it should be pretty quick. From the given point you can have a range on the x and y axis and get all locations within that range (i.e. specify the top left most corner x(a) and y(b) and bottom most right corner x(c) and y(d)).

Then do a query where for points where y >= b AND y <= d AND x >= a AND x <=c. this will be quick assuming you have indexes on the x and y coordinates seperatly. (assuming origin is 0,0 at top left).

You can then increase (or decrease if result is huge) this range by z until the number of points within the result set is >= 1000. Through some trial runs you should be able to come up with a standard deviation and other statistical numbers that will help you determine the size of the rectangle to start with. Your program can also tune its self for this based on the results it gets.

Once you have the rough data set its pretty simple maths to work out the distance between each point and the source point.