# An Optimal Algorithm To Recognize Robinsonian Dissimilarities

3 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
LIS - Laboratoire d'Informatique et Systèmes
4 GANG - Networks, Graphs and Algorithms
Inria de Paris, IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
Abstract : A dissimilarity D on a finite set S is said to be Robinsonian if S can be totally ordered in such a way that, for every $i < j < k, D(i, j) ≤ D(i, k)$ and $D(j, k) ≤ D(i, k)$. Intuitively, D is Robinsonian if S can be represented by points on a line. Recognizing Robinsonian dissimilarities has many applications in se-riation and classification. In this paper, we present an optimal $O(n 2)$ algorithm to recognize Robinsonian dissimilarities, where n is the cardinal of S. Our result improves the already known algorithms.
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Cited literature [41 references]

https://hal.archives-ouvertes.fr/hal-02435793
Contributor : Pascal Préa <>
Submitted on : Saturday, January 11, 2020 - 2:45:26 PM
Last modification on : Thursday, January 23, 2020 - 6:22:13 PM

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• HAL Id : hal-02435793, version 1

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Pascal Préa, Dominique Fortin. An Optimal Algorithm To Recognize Robinsonian Dissimilarities. Journal of Classification, Springer Verlag, 2014. ⟨hal-02435793⟩

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