精确Domatic数问题和精确Conveyor Flow Shop问题的复杂性
Complexity of the Exact Domatic Number Problem and of the Exact Conveyor Flow Shop Problem
摘要：
我们证明了精确版本的domatic数问题是完全的水平的布尔层次NP。在计算机网络领域中出现的domatic数问题，是将给定的图划分为最大数量的不相交控制集的问题。这个数称为图的拓扑数。证明了判定给定图的拓扑数是否为k个给定值之{ \em exactly}的问题对于NP上布尔层次的第2k层是完全的.特别地，对于k = 1，确定给定图的拓扑数是否恰好等于给定整数是DP-完全的。注意DP是NP上布尔层次的第二层。我们得到了类似的结果的精确版本的广义支配集问题和运输机流水车间问题。我们的减少应用瓦格纳的条件足以证明硬度的水平的布尔层次NP。
英文摘要：
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 generalized dominating set problems and of the conveyor flow shop problem. Our reductions apply Wagner's conditions sufficient to prove hardness for the levels of the boolean hierarchy over NP.
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