  Revenue maximization (RM) is one of the most important problems on online
social networks (OSNs), which attempts to find a small subset of users in OSNs
that makes the expected revenue maximized. It has been researched intensively
before. However, most of exsiting literatures were based on non-adaptive
seeding strategy and on simple information diffusion model, such as
IC/LT-model. It considered the single influenced user as a measurement unit to
quantify the revenue. Until Collaborate Game model appeared, it considered
activity as a basic object to compute the revenue. An activity initiated by a
user can only influence those users whose distance are within k-hop from the
initiator. Based on that, we adopt adaptive seed strategy and formulate the
Revenue Maximization under the Size Budget (RMSB) problem. If taking into
account the product's promotion, we extend RMSB to the Revenue Maximization
under the Community Budget (RMCB) problem, where the influence can be
distributed over the whole network. The objective function of RMSB and RMCB is
adatpive monotone and not adaptive submodular, but in some special cases, it is
adaptive submodular. We study the RMSB and RMCB problem under both the speical
submodular cases and general non-submodular cases, and propose RMSBSolver and
RMCBSolver to solve them with strong theoretical guarantees, respectively.
Especially, we give a data-dependent approximation ratio for RMSB problem under
the general non-submodular cases. Finally, we evaluate our proposed algorithms
by conducting experiments on real datasets, and show the effectiveness and
accuracy of our solutions.
