Dendrograms and irreducible prefix codes

  • John McAlpin
  • Christos Nikolopoulos
Track 4: Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 507)


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.


Huffman Code Codeword Length Prefix Code Formal Language Theory Left Subtree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. M.R., Anderberg, "Cluster Analysis for Applications," Academic Press, New York, NY, 1973.Google Scholar
  2. M.A. Harrison, "Introduction to Formal Language Theory," Addison-Wesley, Menlo Park, CA, 1978.Google Scholar
  3. D. Huffman, "A Method for the Construction of Minimal Redundancy Codes," Preceedings IRE 40, 1952.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • John McAlpin
    • 1
  • Christos Nikolopoulos
    • 1
  1. 1.Department of Computer ScienceBradley UniversityPeoria

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