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 seriation 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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