Alphabetic Tree Problem (Optimal Binary Search Trees)
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Description
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
Parameters
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
Space Complexity Graph
Space-Time Tradeoff Improvements
