Journal Article10.1137/0206045
A New Algorithm for Minimum Cost Binary Trees
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TL;DR: The proof of validity is based on finite variational methods and is therefore quite different and somewhat simpler than the proof for the Hu-Tucker algorithm, and yields some additional information about the structure of minimum cost binary trees.
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Abstract: A new algorithm for constructing minimum cost binary trees in $O(n \log n)$ time is presented. The algorithm is similar to the well-known Hu-Tucker algorithm. Our proof of validity is based on finite variational methods and is therefore quite different and somewhat simpler than the proof for the Hu-Tucker algorithm. Our proof also yields some additional information about the structure of minimum cost binary trees. This permits a linear time implementation of our algorithm in a special case.
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A New Proof of the T-C Algorithm
TL;DR: Although the algorithm is simple to state, the associated proof was extremely complicated and long.
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