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An Optimal Algorithm To Recognize Robinsonian Dissimilarities

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  • Pascal Préa
  • Dominique Fortin

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 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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Pascal Préa & Dominique Fortin, 2014. "An Optimal Algorithm To Recognize Robinsonian Dissimilarities," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 351-385, October.
    • Handle: RePEc:spr:jclass:v:31:y:2014:i:3:p:351-385
    DOI: 10.1007/s00357-014-9150-2
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    References listed on IDEAS

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    1. Victor Chepoi & Bernard Fichet & Morgan Seston, 2009. "Seriation in the Presence of Errors: NP-Hardness of l ∞ -Fitting Robinson Structures to Dissimilarity Matrices," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 279-296, December.
    2. Michael Brusco, 2002. "A branch-and-bound algorithm for fitting anti-robinson structures to symmetric dissimilarity matrices," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 459-471, September.
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    Cited by:

    1. Smeulders, B., 2018. "Testing a mixture model of single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 101-113.
    2. Laurent, Monique & Seminaroti, Matteo, 2016. "Similarity-First Search : A New Algorithm With Application to Robinsonian Matrix Recognition," Other publications TiSEM 8468be57-ed46-400c-9c0e-7, Tilburg University, School of Economics and Management.
    3. D. Fortin, 2017. "Robinsonian Matrices: Recognition Challenges," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 191-222, July.
    4. Laurent, Monique & Seminaroti, M. & Tanigawa, Shin-ichi, 2017. "A structural characterization for certifying robinsonian matrices," Other publications TiSEM 5ecebfb8-804e-4267-8c12-b, Tilburg University, School of Economics and Management.
    5. Julio Aracena & Christopher Thraves Caro, 2023. "The weighted sitting closer to friends than enemies problem in the line," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.

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