Correctness of constructing optimal alphabetic trees revisited
نویسندگان
چکیده
منابع مشابه
Correctness of Constructing Optimal Alphabetic Trees Revisited
Several new observations which lead to new correctness proofs of two known algorithms (Hu-Tucker and Garsia-Wachs) for construction of optimal alphabetic trees are presented. A generalized version of the Garsia-Wachs algorithm is given. Proof of this generalized version works in a structured and illustrative way and clari es the usually poorly-understood behavior of both the Hu-Tucker and Garsi...
متن کامل(note) Correctness of Constructing Optimal Alphabetic Trees Revisited
Several new observations which lead to new correctness proofs of two known algorithms (Hu-Tucker and Garsia-Wachs) for construction of optimal alphabetic trees are presented. A generalized version of the Garsia-Wachs algorithm is given. Proof of this generalized version works in a structured and illustrative way and clariies the usually poorly-understood behavior of both the Hu-Tucker and Garsi...
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An algorithm of Knuth for finding an optimal binary tree is extended in several directions to solve related problems. The first case considered is restricting the depth of the tree by some predetermined integer K, and a Kn algorithm is given. Next, for trees of degree tr, rather than binary trees, Kn log tr and n log tr algorithms are found for the restricted and nonrestricted cases, respective...
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We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to be determined.
متن کاملOptimal Integer Alphabetic Trees in Linear Time
We show that optimal alphabetic binary trees can be constructed in O(n) time if the elements of the initial sequence are drawn from a domain that can be sorted in linear time. We describe a hybrid algorithm that combines the bottom-up approach of the original Hu-Tucker algorithm with the top-down approach of Larmore and Przytycka’s Cartesian tree algorithms. The hybrid algorithm demonstrates th...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1997
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(96)00296-4