In this paper, we study a new problem on social network influence maximization. The problem is defined as, given an activatable set A and a targeted set T, finding the k nodes in A with the maximal influence in T. Different from existing influence maximization work which aims to find a small subset of nodes to maximize the spread of influence over the entire network (i.e., from whole to whole), our problem aims to find a small subset of given activatable nodes which can maximize the influence spread to a targeted subset (i.e., from part to part). Theoretically the new frame includes the common influence maximization as its special case. The solution is critical for personalized services, targeted information dissemination, and local viral marketing on social networks, where fully understanding of constraint influence diffusion is essential. To this end, in this paper we propose a constraint influence maximization frame. Specifically, we point out that it is NP-hard and can be approximated by greedy algorithm with guarantee of 1 - 1/e. We also elaborate two special cases: the local one and the global one. Besides, we present the works that are related and beyond. (C) 2014 The Authors. Published by Elsevier B.V.
