432 research outputs found
Gradient Method for Continuous Influence Maximization with Budget-Saving Considerations
Continuous influence maximization (CIM) generalizes the original influence
maximization by incorporating general marketing strategies: a marketing
strategy mix is a vector such that for each
node in a social network, could be activated as a seed of diffusion
with probability , where is a strategy activation
function satisfying DR-submodularity. CIM is the task of selecting a strategy
mix with constraint where is a budget
constraint, such that the total number of activated nodes after the diffusion
process, called influence spread and denoted as , is
maximized. In this paper, we extend CIM to consider budget saving, that is,
each strategy mix has a cost where is a
convex cost function, we want to maximize the balanced sum where is a balance parameter, subject
to the constraint of . We denote this problem as
CIM-BS. The objective function of CIM-BS is neither monotone, nor DR-submodular
or concave, and thus neither the greedy algorithm nor the standard result on
gradient method could be directly applied. Our key innovation is the
combination of the gradient method with reverse influence sampling to design
algorithms that solve CIM-BS: For the general case, we give an algorithm that
achieves -approximation, and for the case
of independent strategy activations, we present an algorithm that achieves
approximation.Comment: To appear in AAAI-20, 43 page
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