Dendrograms and irreducible prefix codes
Dendrograms have been used in cluster analysis and in hierarchical classification problems. In this paper we note that the Huffman method for producing optimal binary codes also produces only dendrograms.
We define an equivalence relation on codes and give an algorithm to produce a prefix code in each class. We also define minimal and maximal total length functions and by exploiting the relationship between irreducible codes and dendrograms, we derive formulas for them. We also derive a measure of code extensibility.
KeywordsHuffman Code Codeword Length Prefix Code Formal Language Theory Left Subtree
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- M.R., Anderberg, "Cluster Analysis for Applications," Academic Press, New York, NY, 1973.Google Scholar
- M.A. Harrison, "Introduction to Formal Language Theory," Addison-Wesley, Menlo Park, CA, 1978.Google Scholar
- D. Huffman, "A Method for the Construction of Minimal Redundancy Codes," Preceedings IRE 40, 1952.Google Scholar