Paper by Erik D. Demaine

Erik D. Demaine, MohammadTaghi Hajiaghayi, Hamid Mahini, David L. Malec, S. Raghavan, Anshul Sawant, and Morteza Zadimoghaddam, “How to Influence People with Partial Incentives”, in Proceedings of the 23rd International World Wide Web Conference (WWW 2014), Seoul, Korea, April 7–11, 2014, pages 937–948.

We study the power of fractional allocations of resources to maximize our influence in a network. This work extends in a natural way the well-studied model by Kleinberg, Kempe, and Tardos (2003), where a designer selects a (small) seed set of nodes in a social network to influence directly, this influence cascades when other nodes reach certain thresholds of neighbor influence, and the goal is to maximize the final number of influenced nodes. Despite extensive study from both practical and theoretical viewpoints, this model limits the designer to a binary choice for each node, with no chance to apply intermediate levels of influence. This model captures some settings precisely, such as exposure to an idea or pathogen, but it fails to capture very relevant concerns in others, for example, a manufacturer promoting a new product by distributing five “20% off” coupons instead of giving away a single free product.

While fractional versions of problems tend to be easier to solve than integral versions, for influence maximization, we show that the two versions have essentially the same computational complexity. On the other hand, the two versions can have vastly different solutions: the added flexibility of fractional allocation can lead to vastly improved influence. Our main theoretical contribution is to show how to adapt the major positive results from the integral case to the fractional case. Specifically, Mossel and Roch (2006) used the submodularity of influence to obtain their integral results; we introduce a new notion of continuous submodularity, and use this to obtain matching fractional results. We conclude that similar algorithms and heuristics from the integral case apply to the fractional case. In practice, we find that the fractional model performs substantially better than the integral model, according to simulations on real-world social network data.

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Last updated March 27, 2017 by Erik Demaine.