  This paper studies a Group Influence with Minimum cost which aims to find a
seed set with smallest cost that can influence all target groups, where each
user is associated with a cost and a group is influenced if the total score of
the influenced users belonging to the group is at least a certain threshold. As
the group-influence function is neither submodular nor supermodular,
theoretical bounds on the quality of solutions returned by the well-known
greedy approach may not be guaranteed. To address this challenge, we propose a
bi-criteria polynomial-time approximation algorithm with high certainty. At the
heart of the algorithm is a novel group reachable reverse sample concept, which
helps speed up the estimation of the group influence function. Finally,
extensive experiments conducted on real social networks show that our proposed
algorithm outperform the state-of-the-art algorithms in terms of the objective
value and the running time.
