Complexity of the Exact Domatic Number Problem and of the Exact Conveyor Flow Shop Problem

Tobias Riege, Jörg Rothe
2004 Theory of Computing Systems  
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 exactly one of k given values is complete for BH 2k
more » ... P), the 2kth 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 = BH 2 (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.
doi:10.1007/s00224-004-1209-8 fatcat:4pnuvyom3jcnpk3xi5skju52v4