I'm trying to determine a fast way of storing a set of objects, each of which have an x and y coordinate value, such that I can quickly retrieve all objects within a certain rectangle or circle.

For small sets of objects (~100) the naive approach of simply storing them in a list, and iterating through it, is relatively quick. However, for much larger groups, that is expectedly slow.

I've tried storing them in a pair of TreeMaps as well, one sorted on the x coordinate, and one sorted on the y coordinate, using this code:

```
xSubset = objectsByX.subSet( minX, maxX );
ySubset = objectsByY.subSet( minY, maxY );
result.addAll( xSubset );
result.retainAll( ySubset );
```

This also works, and is faster for larger sets of objects, but is still slower than I would like.

Part of the problem is also that these objects move around, and need to be inserted back into this storage, which means removing them from and re-adding them to the trees/lists.

I can't help but think there must be better solutions out there.

I'm implementing this in Java, if it makes any difference, though I expect any solution will be more in the form of a useful pattern/algorithm.

## Best Solution

Quadtrees seem to solve the specific problem I asked. Kd-Trees are a more general form, for any number of dimensions, rather than just two.

R-Trees may also be useful if the objects being stored have a bounding rectangle, rather than being just a simple point.

The general term for these type of structures is Spatial Index.

There is a Java implementation of Quadtree and R-Tree.