Abstract

Let \(G = (V,A)\) be a simple directed graph and let \(S\subseteq V \) be a subset of the vertex set \(V \). The set \(S \) is called dominating if for each vertex \(j\in V\setminus S\) there exist at least one \(i\in S \) and an edge from \(i \) to \(j\). A dominating set is called (inclusion) minimal if it contains no smaller dominating set. A dicut \(\{S\rightarrow \overline {S}\} \) is a set of edges \((i,j)\in A \) such that \(i\in S \) and \(j\in V\setminus S \). The weight of a dicut is the total weight of all its edges. The article deals with the problem of finding a dicut \(\{S\rightarrow \overline {S}\} \) with maximum weight among all minimal dominating sets.

中文翻译：

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由最小支配集引起的有向图的最大Dicut

摘要

令\（G =（V，A）\）为简单的有向图，令 \（S \ subseteq V \）为顶点集\（V \）的子集。该组\（S \）被称为主导如果为每个顶点 \（j \ V中\ setminus小号\）的至少一个存在\（I \ S中\）和从边缘\（I \）到\（ j \）。如果主导集不包含更小的主导集，则称其为（包含）极小值。dicut \（\ {S \ rightarrow \ overline {S} \} \）是一组边线\（（i，j）\ in A \）使得\（i \ in S \）和\（j \在V \ setminus S \）。切块的重量是其所有边缘的总重量。本文讨论的问题是，在所有最小支配集中找到最大权重的dicut \（\ {S \ rightarrow \ overline {S} \} \）。