Single and bulk updates in stratified trees: An amortized and worst-case analysis

Abstract

Stratified trees form a family of classes of search trees of special interest because of their generality: they include symmetric binary B-trees, half-balanced trees, and red-black trees, among others. Moreover, stratified trees can be used as a basis for relaxed rebalancing in a very elegant way. The purpose of this paper is to study the rebalancing cost of stratified trees after update operations. The operations considered are the usual insert and delete operations and also bulk insertion, in which a number of keys arc inserted into the same place in the tree. Our results indicate that when insertions, deletions, and bulk insertions are applied in an arbitrary order, the amortized rebalancing cost for single insertions and deletions is constant, and for bulk insertions O(log m), where m is the size of the bulk. The latter is also a bound on the structural changes due to a bulk insertion in the worst case. © Springer-Verlag Berlin Heidelberg 2003.