A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs
Résumé
A dominating set $\mathcal{D}$ of a graph G=(V,E) is a subset of vertices such that every vertex in $V \setminus \mathcal{D}$ has at least one neighbour in $\mathcal{D}$. Moreover if $\mathcal{D}$ is an independent set, i.e. no vertices in $\mathcal{D}$ are pairwise adjacent, then $\mathcal{D}$ is said to be an independent dominating set. Finding a minimum independent dominating set in a graph is an NP-hard problem. We give an algorithm computing a minimum independent dominating set of a graph on n vertices in time $O(1.3575^n)$. Furthermore, we show that $\Omega(1.3247^n)$ is a lower bound on the worst-case running time of this algorithm.