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 O^∗(2ⁿ−^|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 O^∗(1.4143n). In this paper we present a first non-trivial exact algorithm whose running time is in O^∗(1.3645ⁿ). We use our algorithm to solve the Connected Dominating Set problem in O^∗(1.8619ⁿ). This improves the current best known algorithm, which used sophisticated run-time analysis via the measure and conquer technique to solve the problem in O^∗(1.8966ⁿ).