On Huang and Wong’s algorithm for generalized binary split trees

Author:

Chrobak Marek,Golin MordecaiORCID,Munro J. Ian,Young Neal E.

Abstract

AbstractHuang and Wong (Acta Inform 21(1):113–123, 1984) proposed a polynomial-time dynamic-programming algorithm for computing optimal generalized binary split trees. We show that their algorithm is incorrect. Thus, it remains open whether such trees can be computed in polynomial time. Spuler (Optimal search trees using two-way key comparisons, PhD thesis, 1994) proposed modifying Huang and Wong’s algorithm to obtain an algorithm for a different problem: computing optimal two-way comparison search trees. We show that the dynamic program underlying Spuler’s algorithm is not valid, in that it does not satisfy the necessary optimal-substructure property and its proposed recurrence relation is incorrect. It remains unknown whether the algorithm is guaranteed to compute a correct overall solution.

Funder

National Science Foundation

Research Grants Council, University Grants Committee

Publisher

Springer Science and Business Media LLC

Subject

Computer Networks and Communications,Information Systems,Software

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Tight Threshold Bound for Search Trees with 2-Way Comparisons;Lecture Notes in Computer Science;2024

2. Classification via Two-Way Comparisons (Extended Abstract);Lecture Notes in Computer Science;2023

3. A Simple Algorithm for Optimal Search Trees with Two-way Comparisons;ACM Transactions on Algorithms;2022-01-31

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