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Symmetric submodular system: Contractions and Gomory-Hu tree
Information and Computation ( IF 1 ) Pub Date : 2019-09-24 , DOI: 10.1016/j.ic.2019.104479
Saeid Hanifehnezhad , Ardeshir Dolati

Let S=(V,f), be a symmetric submodular system. For two distinct elements s and l of V, let Γ(s,l) denote the set of all subsets of V which separate s from l. By using any Gomory-Hu tree of S we can obtain an element of Γ(s,l) which has minimum value among all the elements of Γ(s,l). This tree can be constructed iteratively by solving |V|1 minimum slseparator 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 S with respect to some subsets of V only by using contraction in a Gomory-Hu tree of S. Furthermore, we obtain some pendant pairs of S and of its contractions by using a Gomory-Hu tree of S.



中文翻译:

对称次模块系统:收缩和Gomory-Hu树

小号=VF,是对称的子模块化系统。对于两个不同的元件小号V,让Γs表示将sl分开V的所有子集的集合。通过使用任何Gomory-Hu树小号 我们可以得到一个元素 Γs 在以下所有元素中具有最小值 Γs。可以通过求解来迭代构造此树|V|-1个 最低 s-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树小号关于V的某些子集,仅通过在小号。此外,我们获得了一些吊坠对小号 和通过使用Gomory-Hu树的收缩 小号

更新日期:2019-09-24
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