Weighted Leaf AVL-Trees

Abstract

A new data structure called a weighted leaf AVL-tree is presented for representing a collection of weighted items drawn from a totally ordered set. It is shown that using this data structure, the average access time of an item is optimal to within a constant factor while the worst-case access time is “logarithmic.” The data structure is a generalization of a leaf AVL-tree to the weighted-item case and retains its restructuring simplicity. It is shown that the data structure supports a number of update operations in a simple and worst-case efficient manner.