Minimum cost seed set for competitive social influence

We wonder that in a competitive environment, how an influence uses the minimum cost to choose seeds such that its influence spread can reach a desired threshold under thwarting from its competitors. At first we take a simple fact into account: the information arriving first has heavy impact, and present Competitive — Independent Cascade (C-IC) model to characterize how different influences competing with others in a social network. We have found that a specific influence's spread is monotone and submodular, and these nice properties make algorithm performance tractable. We then propose Minimum Cost Seed Set problem (MinSeed) to answer our original concern and give a greedy algorithm. We analyze the ratio of greedy algorithm, and give result significantly better than similar ones analyzed by others. Noticing that the computation of real information spread is hard to compute and simple greedy is too time consuming, we design an effective method for estimating information spread in C-IC model, and devise scalable algorithm applying for large social networks. Through simulation on real world datasets, we confirm that, our scalable algorithm outputs seed set with small total cost comparable to that given by simple greedy, with very fast computation.