An in-place priority search tree

One of the classic data structures for storing point sets in R2 is the priority search tree, introduced by Mc- Creight in 1985. We show that this data structure can be made in-place, i.e., it can be stored in an array such that each entry only stores one point of the point set. We show that the standard query operations can be an- swered within the same time bounds as for the original priority search tree, while using only O(1) extra space