The Construction of Huffman Codes is a Submodular ("Convex") Optimization Problem Over a Lattice of Binary Trees

Abstract

We show that the space of all binary Huffman codes for a finite alphabet defines a lattice, ordered by the imbalance of the code trees. Representing code trees as path-length sequences, we show that the imbalance ordering is closely related to a majorization ordering on real-valued sequences that correspond to discrete probability density functions… (More)
DOI: 10.1137/S0097539796311077

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