Solving Capacitated Dominating Set by using covering by subsets and maximum matching

The Capacitated Dominating Set problem is the problem of finding a dominating set of minimum cardinality where each vertex has been assigned a bound on the number of vertices it has capacity to dominate. Cygan et al. showed in 2009 that this problem can be solved in O(n3mnn/3) or in O∗(1.89n) time using maximum matching algorithm. An alternative way to solve this problem is to use dynamic programming over subsets. By exploiting structural properties of instances that cannot be solved fast by the maximum matching approach, and “hiding” additional cost related to considering subsets of large cardinality in the dynamic programming, an improved algorithm is obtained. We show that the Capacitated Dominating Set problem can be solved in O∗(1.8463n) time.