Bernard Fichet

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In this paper, we establish that the following fitting problem is NP-hard: given a finite set X and a dissimilarity measure d on X (d is a symmetric function d from X 2 to the non-negative real numbers and vanishing on the diagonal), we wish to find a Robinsonian dis-similarity d R on X minimizing the l ∞-error ||d − d R || ∞ = max x,y∈X {|d(x, y) − d R (x,(More)
A metric d on a finite set X is called a Kalmanson metric if there exists a circular ordering of points of X, such that dy ;u + d z ;v d y ;z + d u; v for all crossing pairs y uand z vof. We prove that any Kalmanson metric d is an l1-metric, i.e. d can be written as a nonnegative linear combination of split metrics. The splits in the decomposition of d can(More)
Given a vector u and a certain subset K of a real vector space E, the problem of l-approximation involves determining an element u^ in K nearest to u in the sense of the l-error norm. The subdominant u * of u is the upper bound (if it exists) of the set [x # K : x O u] (we let x Oy if all coordinates of x are smaller than or equal to the corresponding(More)
résumé – Dans un cadre général où les concepts de sous-dominante/sur-dominée jouent un rôle fondamental, nous dressons un vaste panorama d'approximations en norme du supremum pour nombre de structures de la classification : ultramétriques (partielles ou non), k-ultramétriques, régressions convexes et isotones. Pour les semi-distances/dissimilarités d'arbre(More)