Extremal properties and morphisms of finite ultrametric spaces and their representing trees

2016/10/26 by O. Dovgoshey, Oleksiy Dovgoshey, Evgeniy Petrov +6 · 1 citation
Computer Science · Mathematics · #Graph theory and applications #Topological and Geometric Data Analysis #advanced mathematical theories #math.MG #msc:05C05 #msc:54E35

paper · pdf · doi:10.48550/arxiv.1610.08282

33 pages, 8 figures

arxiv created 2017/12/16 · arxiv updated 2017/12/19

Abstract

We study extremal properties of finite ultrametric spaces X and related properties of representing trees T_X. The notion of weak similarity for such spaces is introduced and related morphisms of labeled rooted trees are found. It is shown that the finite rooted trees are isomorphic to the rooted trees of nonsingular balls of special finite ultrametric spaces. We also found conditions under which the isomorphism of representing trees T_X and T_Y implies the isometricity of ultrametric spaces X and Y.

Citations

• Nonmetric Multidimensional Scaling: A Numerical Method
• Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis

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