On Ultrametricity, Data Coding, and Computation

• Autores: Fionn Murtagh
• Localización: Journal of classification, ISSN 0176-4268, Vol. 21, Nº 2, 2004, págs. 167-184
• Idioma: inglés
• DOI: 10.1007/s00357-004-0015-y
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• Resumen

  • The triangular inequality is a defining property of a metric space, while the stronger ultrametric inequality is a defining property of an ultrametric space. Ultrametric distance is defined from p-adic valuation. It is known that ultrametricity is a natural property of spaces in the sparse limit. The implications of this are discussed in this article. Experimental results are presented which quantify how ultrametric a given metric space is. We explore the practical meaningfulness of this property of a space being ultrametric. In particular, we examine the computational implications of widely prevalent and perhaps ubiquitous ultrametricity.