**Robust Influence Maximization**

**Xinran He*, University of Southern California; David Kempe, University of Southern California**

#### Abstract

Uncertainty about models and data is ubiquitous in the computational social sciences, and it creates a need for robust social network algorithms, which can simultaneously provide guarantees across a spectrum of models and parameter set-tings. We begin an investigation into this broad domain by studying robust algorithms for the Inﬂuence Maximization problem, in which the goal is to identify a set of k nodes in a social network whose joint inﬂuence on the network is maximized.

We deﬁne a Robust Inﬂuence Maximization framework wherein an algorithm is presented with a set of inﬂuence functions, typically derived from diﬀerent inﬂuence models or diﬀerent parameter settings for the same model. The diﬀerent parameter settings could be derived from observed cascades on diﬀerent topics, under diﬀerent conditions, or at diﬀerent times. The algorithm’s goal is to identify a set of k nodes who are simultaneously inﬂuential for all inﬂuence functions, compared to the (function-speciﬁc) optimum solutions.

We show strong approximation hardness results for this problem unless the algorithm gets to select at least a logarithmic factor more seeds than the optimum solution. However, when enough extra seeds may be selected, we show that techniques of Krause et al. can be used to approximate the optimum robust inﬂuence to within a factor of 1 − 1/e. We evaluate this bicriteria approximation algorithm against natural heuristics on several real-world data sets. Our experiments indicate that the worst-case hardness does not necessarily translate into bad performance on real-world data sets; all algorithms perform fairly well.

**Filed under: Graph Mining and Social Networks**