On k-Dimensional Balanced Binary Trees

An amortized analysis of the insertion and deletion algorithms of k-dimensional balanced binary trees (kBB-trees) is performed. It is shown that the total rebalancing time for a mixed sequence of m insertions and deletions in a kBB-tree of size n is O(k(m+n)). Based on 2BB-trees, a self-organizing tree, called a self-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 of kBBtrees leads to the result that the total update time for a mixed sequence of m accesses, insertions, and (restricted) deletions in a self-organizing balanced binary tree initially storing n data items is O(m+n). ] 1996