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Given a social network $G$, the profit maximization (PM) problem asks for aset of seed nodes to maximize the profit, i.e., revenue of influence spreadless the cost of seed selection. The target profit maximization (TPM) problem,which generalizes the PM problem, aims to select a subset of seed nodes from atarget user set $T$ to maximize the profit. Existing algorithms for PM mostlyconsider the nonadaptive setting, where all seed nodes are selected in onebatch without any knowledge on how they may influence other users. In thispaper, we study TPM in adaptive setting, where the seed users are selectedthrough multiple batches, such that the selection of a batch exploits theknowledge of actual influence in the previous batches. To acquire an overallunderstanding, we study the adaptive TPM problem under both the oracle modeland the noise model, and propose ADG and AddATP algorithms to address them withstrong theoretical guarantees, respectively. In addition, to better handle thesampling errors under the noise model, we propose the idea of hybrid errorbased on which we design a novel algorithm HATP that boosts the efficiency ofAddATP significantly. We conduct extensive experiments on real social networksto evaluate the performance, and the experimental results strongly confirm thesuperiorities and effectiveness of our solutions.

Efficient Approximation Algorithms for Adaptive Target Profit Maximization