Onk-Dimensional Balanced Binary Trees

Abstract

An amortized analysis of the insertion and deletion algorithms ofk-dimensional balanced binary trees (kBB-trees) is performed. It is shown that the total rebalancing time for a mixed sequence ofminsertions and deletions in akBB-tree of sizenisO(k(m+n)). Based on 2BB-trees, a self-organizing tree, called aself-organizing balanced binary tree, is defined. It is shown that the average access time for an item stored in the tree is optimal to within a constant factor, while the worst-case access time is logarithmic. The amortized analysis ofkBB-trees leads to the result that the total update time for a mixed sequence ofmaccesses, insertions, and (restricted) deletions in a self-organizing balanced binary tree initially storingndata items isO(m+n)