  Influence maximization(IM) problem is to find a seed set in a social network
which achieves the maximal influence spread. This problem plays an important
role in viral marketing. Numerous models have been proposed to solve this
problem. However, none of them considers the attributes of nodes. Paying all
attention to the structure of network causes some trouble applying these models
to real-word applications.
  Motivated by this, we present weighted independent cascade (WIC) model, a
novel cascade model which extends the applicability of independent cascade(IC)
model by attaching attributes to the nodes. The IM problem in WIC model is to
maximize the value of nodes which are influenced. This problem is NP-hard. To
solve this problem, we present a basic greedy algorithm and Weight Reset(WR)
algorithm. Moreover, we propose Bounded Weight Reset(BWR) algorithm to make
further effort to improve the efficiency by bounding the diffusion node
influence. We prove that BWR is a fully polynomial-time approximation
scheme(FPTAS). Experimentally, we show that with additional node attribute, the
solution achieved by WIC model outperforms that of IC model in nearly 90%. The
experimental results show that BWR can achieve excellent approximation and
faster than greedy algorithm more than three orders of magnitude with little
sacrifice of accuracy. Especially, BWR can handle large networks with millions
of nodes in several tens of seconds while keeping rather high accuracy. Such
result demonstrates that BWR can solve IM problem effectively and efficiently.
