Viral Marketing for Product Cross-sell through Social Networks Ramasuri Narayanam and Amit A. Nanavati IBM Research, India. Email ID: {nramasuri,namit}@in.ibm.com Abstract. The well known influence maximization problem [1] (or viral market- ing 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 prob- lem 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 of- ten has budget constraints, the initial seeds have to be chosen within a given budget. We refer to this generalized problem setting as Budgeted Influence Maxi- mization 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. Keywords Social networks, influence maximization, cross-sell, budget constraint, matroid theory, costs, benefits, and submodularity. 1 Introduction The phenomenon of viral marketing is to exploit the social connections among the individuals to promote awareness for new products [2–4]. One of the key issues in viral marketing through social networks is to select a set of influential seed members (also called as initial seeds) in the social network and give them free samples of the product (or provide promotional offers) to trigger cascade of influence over the network [5]. The problem is, given an integer k, how should we choose a set of k initial seeds so