Acta Informatica

, Volume 23, Issue 3, pp 311–323 | Cite as

NP-hard problems in hierarchical-tree clustering

  • Mirko Křivánek
  • Jaroslav Morávek


We consider a class of optimization problems of hierarchical-tree clustering and prove that these problems are NP-hard. The sequence of polynomial reductions and/or transformations used in our proof is based on relatively laborious graph-theoretical constructions and starts in the NP-complete problem of 3-dimensional matching. Using our main result we establish the NP-completeness of a problem of the best approximation of a symmetric relation on a finite set by an equivalence relation, thus answering in the negative a question proposed implicitly by C.T. Zahn.


Information System Operating System Data Structure Communication Network Information Theory 
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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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Mirko Křivánek
    • 1
  • Jaroslav Morávek
    • 2
  1. 1.Research Institute of Mathematical MachinesPraha 1ČSSR
  2. 2.Mathematical InstituteCzechoslovak Academy of SciencesPraha 1CSSR

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