On the degree of ultrametricity

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Abstract
Using the notion of the subdominant ultrametric, the degree of ultrametricity D of a given metric space (e.g. phase space) is introduced. A simple and efficient method for the calculation of D is outlined. D is shown to provide a simple quantitative measure of the deviation from exact ultrametricity. Explicit examples are used to illustrate this notion which is argued to be of some interest in statistical-mechanical models and combinatorial optimization problems