An efficient local search algorithm for minimum positive influence dominating set problem

In graph theory, the minimum dominating set (MDS) problem is one of the most important combinatorial optimization problems. An important extension of the MDS problem is the minimum positive influence dominating set (MPIDS) problem; it has extensive applications, especially in social networks. Compared with MDS, which is used to develop many heuristic and exact algorithms and to efficiently solve massive graphs with millions of vertices, the MPIDS algorithms generally work on small-scale instances and are not applicable for massive graphs. To solve the MPIDS problems with different scale instances, this study proposes an efficient local search algorithm based on three main ideas. First, a reduction-based initialization method is used to fix portions of vertices inside or outside the candidate solution; it avoids exploring redundant search spaces. Second, by fully considering the characteristic of the MPIDS problem, a novel vertex exchange strategy is designed based on two types of scoring functions. Third, a general local search framework based on a two -level satisfaction judgment mechanism is proposed to improve the performance of the search procedure. The experimental results show that the proposed algorithm performs much better than several state-of-the-art MPIDS algorithms on both conventional benchmarks and a suite of massive graphs in terms of solution quality.