Fernández Elena, Kuziak Dorota, Munoz-Marquez Manuel, Yero Ismael G
Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Cádiz , Spain.
Departamento de Matemáticas, Universidad de Cádiz, Cádiz , Spain.
Sci Rep. 2023 Nov 4;13(1):19090. doi: 10.1038/s41598-023-40165-x.
This work focuses on the [Formula: see text]-anonymity of some networks as a measure of their privacy against active attacks. Two different types of networks are considered. The first one consists of graphs with a predetermined structure, namely cylinders, toruses, and 2-dimensional Hamming graphs, whereas the second one is formed by randomly generated graphs. In order to evaluate the [Formula: see text]-anonymity of the considered graphs, we have computed their k-metric antidimension. To this end, we have taken a combinatorial approach for the graphs with a predetermined structure, whereas for randomly generated graphs we have developed an integer programming formulation and computationally tested its implementation. The results of the combinatorial approach, as well as those from the implementations indicate that, according to the [Formula: see text]-anonymity measure, only the 2-dimensional Hamming graphs and some general random dense graphs are achieving some higher privacy properties.
这项工作聚焦于某些网络的[公式：见文本]-匿名性，以此作为衡量其抵御主动攻击时隐私性的一种指标。我们考虑了两种不同类型的网络。第一种由具有预定结构的图组成，即圆柱体、环面和二维汉明图，而第二种是由随机生成的图构成。为了评估所考虑图的[公式：见文本]-匿名性，我们计算了它们的k - 度量反维数。为此，对于具有预定结构的图，我们采用了组合方法，而对于随机生成的图，我们开发了一个整数规划公式并对其实现进行了计算测试。组合方法的结果以及实现的结果表明，根据[公式：见文本]-匿名性指标，只有二维汉明图和一些一般的随机密集图具有较高的隐私特性。
