OPTIMAL OPERATIONS ON RED-BLACK TREES

We show here that on a red-black tree with only two pointers — left pointing to the left child and right pointing to the right child — for each node, some standard operations such as searching, deletion, and insertion can be performed in O( log n) time, in the worst case, using only O(1) auxiliary space. No procedures do these fundamental operations more efficiently in time and space. The time and the space bounds of our algorithms are both optimal. The result is achieved by applying the pointer altering technique on red-black trees. The usefulness of the technique is further illustrated in this paper. Efficient implementations of the algorithms are also addressed here.