  Motivated by online social networks that are linked together through
overlapping users, we study the influence maximization problem on a multiplex,
with each layer endowed with its own model of influence diffusion. This problem
is a novel version of the influence maximization problem that necessitates new
analysis incorporating the type of propagation on each layer of the multiplex.
We identify a new property, generalized deterministic submodular, which when
satisfied by the propagation in each layer, ensures that the propagation on the
multiplex overall is submodular -- for this case, we formulate ISF, the greedy
algorithm with approximation ratio $(1 - 1/e)$. Since the size of a multiplex
comprising multiple OSNs may encompass billions of users, we formulate an
algorithm KSN that runs on each layer of the multiplex in parallel. KSN takes
an $\alpha$-approximation algorithm A for the influence maximization problem on
a single-layer network as input, and has approximation ratio
$\frac{(1-\epsilon)\alpha}{(o+1)k}$ for arbitrary $\epsilon > 0$, $o$ is the
number of overlapping users, and $k$ is the number of layers in the multiplex.
Experiments on real and synthesized multiplexes validate the efficacy of the
proposed algorithms for the problem of influence maximization in the
heterogeneous multiplex. Implementations of ISF and KSN are available at
http://www.alankuhnle.com/papers/mim/mim.html.
