Information and Computation ( IF 1 ) Pub Date : 2019-09-24 , DOI: 10.1016/j.ic.2019.104479 Saeid Hanifehnezhad , Ardeshir Dolati
Let , be a symmetric submodular system. For two distinct elements s and l of V, let denote the set of all subsets of V which separate s from l. By using any Gomory-Hu tree of we can obtain an element of which has minimum value among all the elements of . This tree can be constructed iteratively by solving minimum separator problem. Pendant pairs of a symmetric submodular system play a key role in finding a minimizer of this system. In this paper, we obtain a Gomory-Hu tree of a contraction of with respect to some subsets of V only by using contraction in a Gomory-Hu tree of . Furthermore, we obtain some pendant pairs of and of its contractions by using a Gomory-Hu tree of .
中文翻译:
对称次模块系统:收缩和Gomory-Hu树
让 ,是对称的子模块化系统。对于两个不同的元件小号和升的V,让表示将s与l分开的V的所有子集的集合。通过使用任何Gomory-Hu树 我们可以得到一个元素 在以下所有元素中具有最小值 。可以通过求解来迭代构造此树 最低 分隔符问题。对称次模块系统的垂线对在寻找该系统的最小化器中起关键作用。在本文中,我们获得了收缩的Gomory-Hu树关于V的某些子集,仅通过在。此外,我们获得了一些吊坠对 和通过使用Gomory-Hu树的收缩 。