Viral Marketing for Product Cross-Sell through Social Networks

The well known influence maximization problem [1] (or viral marketing through social networks) deals with selecting a few influential initial seeds to maximize the awareness of product(s) over the social network. In this paper, we introduce a novel and generalized version of the influence maximization problem that considers simultaneously the following three practical aspects: (i) Often cross-sell among products is possible, (ii) Product specific costs (and benefits) for promoting the products have to be considered, and (iii) Since a company often has budget constraints, the initial seeds have to be chosen within a given budget. We refer to this generalized problem setting as Budgeted Influence Maximization with Cross-sell of Products (B-IMCP). To the best of our knowledge, we are not aware of any work in the literature that addresses the B-IMCP problem which is the subject matter of this paper. Given a fixed budget, one of the key issues associated with the B-IMCP problem is to choose the initial seeds within this budget not only for the individual products, but also for promoting cross-sell phenomenon among these products. In particular, the following are the specific contributions of this paper: (i) We propose an influence propagation model to capture both the cross-sell phenomenon and product specific costs and benefits; (ii) As the B-IMCP problem is NP-hard computationally, we present a simple greedy approximation algorithm and then derive the approximation guarantee of this greedy algorithm by drawing upon the results from the theory of matroids; (iii) We then outline two efficient heuristics based on well known concepts in the literature. Finally, we experimentally evaluate the proposed approach for the B-IMCP problem using a few well known social network data sets such as WikiVote data set, Epinions, and Telecom call detail records data.