On ultrametricity, data coding, and computation
On ultrametricity, data coding, and computation
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DOI：
10.1007/s00357-004-0015-y
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发表时间：
2004-01-01
影响因子：
2
通讯作者：
Murtagh, F
中科院分区：
文献类型：
--
作者：
Murtagh, F
三角不等式是度量空间的一个定义性性质，而强超度量不等式是超度量空间的一个定义性性质。超度量距离是由p进值定义的。在稀疏极限下，超度量性是空间的一种自然性质。本文将讨论其含义。给出了量化给定度量空间的超度量程度的实验结果。我们探讨了超度量空间的这一性质的实际意义。特别是，我们研究了广泛流行的和可能无处不在的超对称性的计算含义。
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.