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Combinatorial optimisation and hierarchical classifications

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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.

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Authors and Affiliations

  1. CAMS, EHESS, UMR CNRS 8557, Paris, France

    J.-P. Barthélemy

  2. ENST Bretagne, Dept. LUSSI and TAMCIC, FRE CNRS 2658, Paris, France

    J.-P. Barthélemy & F. Brucker

  3. ENSIETA, Laboratoire E³I², Paris, France

    C. Osswald

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  1. J.-P. Barthélemy
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  3. C. Osswald
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This article appeared in 4OR 2, 179–219, 2004.

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Barthélemy, JP., Brucker, F. & Osswald, C. Combinatorial optimisation and hierarchical classifications. Ann Oper Res 153, 179–214 (2007). https://doi.org/10.1007/s10479-007-0174-4

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