Partition of graph to locate a point

Question

I have an area which was already partitioned into tens of sub-areas (think like a country divided into states).

Now I have a point coordinate, what is the best algorithm to tell me which state the point in?

Of course I can match sub-area by sub-area but that's stupid because I have to search through half of them in average right?

Is there an algorithm to determine how to group several adjacent sub-area together to facilitate search, so as to optimize the number of search?

Answer 1

I would start by eliminating all areas that cannot have the point inside of them.

Let's assume that you have a 2D Cartesian coordinate system, you have a point as a 2D-vector and the areas are described as a collection of their boundary points.

Then you can sort the areas by their smallest and largest x and y coordinate (in total 4 ways of sorting). You can eliminate all areas which have their smallest x coordinate bigger than the x coordinate of your point etc.

After that, you can check the remaining polygons with a simple ray-casting algorithm and you should be good.

This is very efficient if you have a structure which keeps the areas sorted in all the different directions because you can eliminate the areas in logarithmic time.