An algorithm for influence maximization in a two-terminal series parallel graph and its application to a real network

Abstract

We developed an algorithm to exactly solve an influence maximization problem (MaxInf) for a two-terminal series parallel graph (TTSPG) in the independent cascade model. The class of TTSPGs can be considered as a class wider than that of trees, only for which an efficient exact solver of this problem has been developed so far. Our algorithm calculates candidate node sets in the divide-and-conquer manner keeping the number of them as small as possible by efficiently eliminating unnecessary ones in merge of subproblems’ solutions. Furthermore, we propose a way of converting an arbitrary network to a TTSPG with edges important for propagation to apply our method to real networks. According to our empirical results, our method is significantly faster than the greedy approximation algorithm for MAXINF of a TTSPG. We also demonstrate improvement of solutions by converting to TTSPGs instead of trees using real networks made from DBLP datasets.