On Ultrametricity,Data Coding,and Computation |
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Authors: | Fionn Murtagh |
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Institution: | (1) Royal Holloway University of London, England |
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Abstract: | 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. |
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Keywords: | |
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