Quasi-ultrametrics and their 2-ball hypergraphs
Quasi-ultrametrics and their 2-ball hypergraphs
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DOI：
10.1016/s0012-365x(98)00067-3
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发表时间：
1998-10-28
影响因子：
0.8
通讯作者：
Fichet, B
中科院分区：
文献类型：
--
作者：
Diatta, J;Fichet, B
拟超度量是满足两个球(球对的交集)两个条件的相异函数：包含条件和直径条件。证明了任意拟超度量的2球超图是无三角形的。在这样的超图上加上一些经典的约束条件，我们得到了所谓的拟层次。此外，著名的指标族和超度量之间的双射(Benzecri，1973；Jardine等人，1967和Johnson，1967)被推广到指标族和拟超度量。这一结果统一了前面提到的双射和将索引伪谱系与强Robinsson不同点相联系的双射(Fichet，1986)。它还被推广到分层拟谱系和拟超度量预约阵中。(C)1998 Elsevier Science B.V.保留所有权利。
A quasi-ultrametric is a dissimilarity function satisfying two conditions involving 2-balls (intersections of pairs of balls): the inclusion and the diameter conditions. The 2-ball hypergraph of any quasi-ultrametric is shown to be triangle-free. Adding some classical constraints to such a hypergraph, we obtain the so-called quasi-hierarchies. Moreover, the well-known bijection between indexed hierarchies and ultrametrics (Benzecri, 1973; Jardine et al., 1967 and Johnson, 1967) is extended to indexed quasi-hierarchies and quasi-ultrametrics. This result unifies the previously-mentioned bijection and the one relating indexed pseudo-hierarchies to strongly Robinsonian dissimilarities (Fichet, 1986). It is also generalized in terms of stratified quasi-hierarchies and quasi-ultrametric preordonnances. (C) 1998 Elsevier Science B.V. All rights reserved.