An exact algorithm for connected red-blue dominating set

In the Connected Red-Blue Dominating Set problem we are given a graph G whose vertex set is partitioned into two parts R and B (red and blue vertices), and we are asked to find a connected subgraph induced by a subset S of B such that each red vertex of G is adjacent to some vertex in S. The problem can be solved in $\mathcal{O}^*(2^{n - |B|})$ time by reduction to the Weighted Steiner Tree problem. Combining exhaustive enumeration when |B| is small with the Weighted Steiner Tree approach when |B| is large, solves the problem in $\mathcal{O}^*(1.4143^n)$. In this paper we present a first non-trivial exact algorithm whose running time is in $\mathcal{O}^*(1.3645^n)$. We use our algorithm to solve the Connected Dominating Set problem in $\mathcal{O}^*(1.8619^n)$. This improves the current best known algorithm, which used sophisticated run-time analysis via the measure and conquer technique to solve the problem in $\mathcal{O}^*(1.8966^n)$.