期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2002
卷号：2002
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We prove that the exact versions of the domatic number problem are complete for the levels of the boolean hierarchy over NP. The domatic number problem, which arises in the area of computer networks, is the problem of partitioning a given graph into a maximum number of disjoint dominating sets. This number is called the domatic number of the graph. We prove that the problem of determining whether or not the domatic number of a given graph is {\em exactly\/} one of k given values is complete for the 2k-th level of the boolean hierarchy over NP. In particular, for k = 1, it is DP-complete to determine whether or not the domatic number of a given graph equals exactly a given integer. Note that DP is the second level of the boolean hierarchy over NP. We obtain similar results for the exact versions of the conveyor flow shop problem, which arises in real-world applications in the wholesale business, where warehouses are supplied with goods from a central storehouse. Our reductions apply Wagner's conditions sufficient to prove hardness for the levels of the boolean hierarchy over NP.
关键词：Boolean hierarchy , completeness , Computational Complexity , conveyor flow shop problem , domatic number problem
