Given a set of $n$ intervals on a line, there is a $O(n \log n)$ algorithm to find intervals which are contained in other intervals (e.g., Manber, Using induction to design algorithms, 1988).  Is there a $O(n \log n)$ algorithm for axis-aligned rectangles in higher dimensions?I did some search on the internet, and tried to think about it myself, but could not find a generalization for higher dimensions.  For example, given $n$ axis-aligned rectangles on the plane, the task is to find which rectangles are contained in other rectangles. 
Efficient algorithm for rectangle containment
algorithms;computational geometry