An Optimal Algorithm To Recognize Robinsonian Dissimilarities

Pascal Préa 1, 2, 3 Dominique Fortin 4
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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Pascal Préa, Dominique Fortin. An Optimal Algorithm To Recognize Robinsonian Dissimilarities. Journal of Classification, Springer Verlag, 2014. ⟨hal-02435793⟩

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