# On Huang and Wong's Algorithm for Generalized Binary Split Trees

## TL;DR

This paper critically examines Huang and Wong's polynomial-time algorithm for generalized binary split trees, demonstrating its incorrectness and highlighting unresolved questions about the problem's computational complexity.

## Contribution

The paper proves that Huang and Wong's algorithm for generalized binary split trees is incorrect and shows that Spuler's modification for two-way comparison trees also lacks validity.

## Key findings

- Huang and Wong's algorithm is incorrect
- Spuler's algorithm does not satisfy optimal substructure
- The complexity of computing generalized binary split trees remains open

## Abstract

Huang and Wong [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 [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.