  Influence Maximization (IM) is a famous topic in mobile networks and social
computing, which aims at finding a small subset of users to maximize the
influence spread through online information cascade. Recently, some careful
researchers paid attention to diversity of information dissemination,
especially community-aware diversity, and formulated the diversified IM
problem. The diversity is ubiquitous in a lot of real-world applications, but
they are all based on a given community structure. In social networks, we can
form heterogeneous community structures for the same group of users according
to different metrics. Therefore, how to quantify the diversity based on
multiple community structures is an interesting question. In this paper, we
propose the Composite Community-Aware Diversified IM (CC-DIM) problem, which
aims at selecting a seed set to maximize the influence spread and the composite
diversity over all possible community structures under consideration. To
address the NP-hardness of CC-DIM problem, we adopt the technique of reverse
influence sampling and design a random Generalized Reverse Reachable (G-RR) set
to estimate the objective function. The composition of a random G-RR set is
much more complex than the RR set used for the IM problem, which will lead to
inefficiency of traditional sampling-based approximation algorithms. Because of
this, we further propose a two-stage algorithm, Generalized HIST (G-HIST). It
can not only return a $(1-1/e-\varepsilon)$ approximate solution with at least
$(1-\delta)$ probability, but also improve the efficiency of sampling and ease
the difficulty of searching by significantly reducing the average size of G-RR
sets. Finally, we evaluate our G-HIST on real datasets against existing
algorithms. The experimental results show the effectiveness of our proposed
algorithm and its superiority over other baseline algorithms.
