We consider Upper Domination, the problem of finding the minimal dominating set of maximum cardinality. Very few exact algorithms have been described for solving Upper Domination. In particular, no binary programming formulations for Upper Domination have been described in literature, although such formulations have proved quite successful for other kinds of domination problems. We introduce two such binary programming formulations, and show that both can be improved with the addition of extra constraints which reduce the number of feasible solutions. We compare the performance of the formulations on various kinds of graphs, and demonstrate that (a) the additional constraints improve the performance of both formulations, and (b) the first formulation outperforms the second in most cases, although the second performs better for very sparse graphs. Also included is a short proof that the upper domination number of any generalized Petersen graph P(n,k) is equal to n.

翻译：我们考虑上支配问题，即寻找最大基数的极小支配集。目前鲜有精确算法被描述用于解决上支配问题。特别地，文献中尚未报道过针对上支配问题的二进制规划公式，尽管此类公式在其他类型的支配问题中已被证明相当成功。我们引入了两种这样的二进制规划公式，并表明两者均可通过添加额外约束来改进，从而减少可行解的数量。我们比较了这些公式在不同类型图上的性能，并证明：(a) 额外约束提升了两种公式的性能；(b) 在大多数情况下，第一种公式优于第二种，尽管第二种在非常稀疏的图上表现更佳。此外，本文还包含一个简短证明，即任意广义彼得森图P(n,k)的上支配数等于n。