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

@article{Parker1999TheCO,
  title={The Construction of Huffman Codes is a Submodular ("Convex") Optimization Problem Over a Lattice of Binary Trees},
  author={Douglas Stott Parker and Prasad Ram},
  journal={SIAM J. Comput.},
  year={1999},
  volume={28},
  pages={1875-1905}
}
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. Furthermore, this tree imbalance is a partial ordering that is consistent with the total orderings given by either the external path length (sum of… CONTINUE READING

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