A note on the computational complexity of hierarchical overlapping clustering. (English) Zbl 0581.62052

In this paper the computational complexity of the problem of the approximation of a given dissimilarity measure on a finite set X by a k- ultrametric on X and by a Robinson dissimilarity measure on X is investigated. It is shown that the underlying decision problems are NP- complete.


62H30 Classification and discrimination; cluster analysis (statistical aspects)
68Q25 Analysis of algorithms and problem complexity
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[1] E. Diday: Une représentation visuelle des classes empiétantes - les pyramides. Rap. de Recherche No 291, INRIA, Rocquencourt, 1984. · Zbl 0592.62052
[2] M. R. Garey, D. S. Johnson: Computers and Intractability: a Guide to the Theory of NP-completeness. W. H. Freeman, San Francisco, 1979. · Zbl 0411.68039
[3] L. Hubert: A set-theoretical approach to the problem of hierarchical clustering. Journal of Mathematical Psychology, 15 (1977), 1 pp. 70–88. · Zbl 0358.62042
[4] N. Jardine, R. Sibson: Mathematical Taxonomy. Wiley, London, 1971. · Zbl 0322.62065
[5] R. M. Karp: Red liability among combinatorial problems. Complexity of computer computations, Proceedings, Plenum Press 1972. Editors: R. E. Miller, J. W. Thatcher.
[6] M. Křivánek, J. Morávek: On NP-hardness in hierarchical clustering. COMPSTAT 1984, Proceedings, Physica-Verlag 1984. Editors: T. Havránek, Z. Šidák, M. Novák. · Zbl 0577.62058
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