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Combinatorial optimisation and hierarchical classifications

Author

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  • J.-P. Barthélemy
  • F. Brucker
  • C. Osswald

Abstract

This paper is devoted to some selected topics relating Combinatorial Optimization and Hierarchical Classification. It is oriented toward extensions of the standard classification schemes (the hierarchies): pyramids, quasi-hierarchies, circular clustering, rigid clustering and others. Bijection theorems between these models and dissimilarity models allow to state some clustering problems as optimization problems. Within the galaxy of optimization we have especially discussed the following: NP-completeness results and search for polynomial instances; problems solved in a polynomial time (e.g. subdominant theory); design, analysis and applications of algorithms. In contrast with the orientation to “new” clustering problems, the last part discusses some standard algorithmic approaches. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • J.-P. Barthélemy & F. Brucker & C. Osswald, 2007. "Combinatorial optimisation and hierarchical classifications," Annals of Operations Research, Springer, vol. 153(1), pages 179-214, September.
    • Handle: RePEc:spr:annopr:v:153:y:2007:i:1:p:179-214:10.1007/s10479-007-0174-4
    DOI: 10.1007/s10479-007-0174-4
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    4. J. Carroll, 1976. "Spatial, non-spatial and hybrid models for scaling," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 439-463, December.
    5. Victor Chepoi & Bernard Fichet, 1997. "Recognition of Robinsonian dissimilarities," Journal of Classification, Springer;The Classification Society, vol. 14(2), pages 311-325, September.
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