Restructuring ordered binary trees

We consider the problem of restructuring an ordered binary tree T , preserving the in-order sequence of its nodes, so as to reduce its height to some target value h. Such a restructuring necessarily involves the downward displacement of some of the nodes of T . Our results, focusing both on the maximum displacement over all nodes and on the maximum displacement over leaves only, provide (i) an explicit tradeoff between the worst-case displacement and the height restriction (including a family of trees that exhibit the worst-case displacements) and (ii) efficient algorithms to achieve height-restricted restructuring while minimizing the maximum node displacement. 2003 Elsevier Inc. All rights reserved.

• Type: Conference
• Year: 2000
• Where: SODA
• Authors: William S. Evans, David G. Kirkpatrick
• Keywords: Algorithms, Downward Displacement, Maximum Displacement, SODA 2000, Worst-case Displacements