Abstract
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.
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References
M.R., Anderberg, "Cluster Analysis for Applications," Academic Press, New York, NY, 1973.
M.A. Harrison, "Introduction to Formal Language Theory," Addison-Wesley, Menlo Park, CA, 1978.
D. Huffman, "A Method for the Construction of Minimal Redundancy Codes," Preceedings IRE 40, 1952.
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© 1991 Springer-Verlag Berlin Heidelberg
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McAlpin, J., Nikolopoulos, C. (1991). Dendrograms and irreducible prefix codes. In: Sherwani, N.A., de Doncker, E., Kapenga, J.A. (eds) Computing in the 90's. Great Lakes CS 1989. Lecture Notes in Computer Science, vol 507. Springer, New York, NY. https://doi.org/10.1007/BFb0038490
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DOI: https://doi.org/10.1007/BFb0038490
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