The Optimal Alphabetic Tree problem revisited
- Teresa M. PrzytyckaAffiliated withDepartment of Mathematics and Computer Science, Odense University
- , Lawrence L. LarmoreAffiliated withDepartment of Computer Science, University of Nevada Las Vegas
The Optimal Alphabetic Binary Tree (OABT) problem is equivalent to the Optimal Binary Search Tree problem with the restriction that all data are in the leaves. The problem can be solved in O(n log n) time, while the best known lower bound is Ω(n).
The main result of this paper is an O(n√log n)-time algorithm for the integer OABT problem. As a side effect we obtain an O(n log k)-time algorithm for the general OABT problem, where k is a number at most as large as the number of local minima. This algorithm gives rise to linear time algorithms for some special cases. As a corollary, we obtain an O(nL)-time algorithm for the integer case of the optimal height-limited alphabetic tree problem, where L is the height limitation.
- The Optimal Alphabetic Tree problem revisited
- Book Title
- Automata, Languages and Programming
- Book Subtitle
- 21st International Colloquium, ICALP 94 Jerusalem, Israel, July 11–14, 1994 Proceedings
- pp 251-262
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
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