Indexed Geometric Jumbled Pattern Matching

We consider how to preprocess n colored points in the plane such that later, given a multiset of colors, we can quickly find an axisaligned rectangle containing a subset of the points with exactly those colors, if one exists. We first give an index that uses o(n) space and o(n) query time when there are O(1) distinct colors. We then restrict our attention to the case in which there are only two distinct colors. We give an index that uses O(n) bits and O(1) query time to detect whether there exists a matching rectangle. Finally, we give a O(n)-space index that returns a matching rectangle, if one exists, in O(lg n/ lg lgn) time.