Alphabetic Tree Problem (Optimal Binary Search Trees)

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A variant of the OBST problem is when only the gaps have nonzero access probabilities, and is called the optimal alphabetic tree problem.

Related Problems

Generalizations: Optimal Binary Search Tree Problem

Related: Approximate OBST, Huffman Encoding


$n$: number of elements

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Klawe; Mumey 1993 $O(n)$ $O(n)$ Exact Deterministic Time
Garsia–Wachs algorithm 1977 $O(n \log n)$ $O(n)$ Exact Deterministic Time & Space
Hu–Tucker algorithm 1971 $O(n \log n)$ $O(n)$ Exact Deterministic Time & Space

Time Complexity Graph

Optimal Binary Search Trees - Alphabetic Tree Problem - Time.png