116,813 research outputs found

    Influence Maximization: Near-Optimal Time Complexity Meets Practical Efficiency

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    Given a social network G and a constant k, the influence maximization problem asks for k nodes in G that (directly and indirectly) influence the largest number of nodes under a pre-defined diffusion model. This problem finds important applications in viral marketing, and has been extensively studied in the literature. Existing algorithms for influence maximization, however, either trade approximation guarantees for practical efficiency, or vice versa. In particular, among the algorithms that achieve constant factor approximations under the prominent independent cascade (IC) model or linear threshold (LT) model, none can handle a million-node graph without incurring prohibitive overheads. This paper presents TIM, an algorithm that aims to bridge the theory and practice in influence maximization. On the theory side, we show that TIM runs in O((k+\ell) (n+m) \log n / \epsilon^2) expected time and returns a (1-1/e-\epsilon)-approximate solution with at least 1 - n^{-\ell} probability. The time complexity of TIM is near-optimal under the IC model, as it is only a \log n factor larger than the \Omega(m + n) lower-bound established in previous work (for fixed k, \ell, and \epsilon). Moreover, TIM supports the triggering model, which is a general diffusion model that includes both IC and LT as special cases. On the practice side, TIM incorporates novel heuristics that significantly improve its empirical efficiency without compromising its asymptotic performance. We experimentally evaluate TIM with the largest datasets ever tested in the literature, and show that it outperforms the state-of-the-art solutions (with approximation guarantees) by up to four orders of magnitude in terms of running time. In particular, when k = 50, \epsilon = 0.2, and \ell = 1, TIM requires less than one hour on a commodity machine to process a network with 41.6 million nodes and 1.4 billion edges.Comment: Revised Sections 1, 2.3, and 5 to remove incorrect claims about reference [3]. Updated experiments accordingly. A shorter version of the paper will appear in SIGMOD 201

    Shaping Social Activity by Incentivizing Users

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    Events in an online social network can be categorized roughly into endogenous events, where users just respond to the actions of their neighbors within the network, or exogenous events, where users take actions due to drives external to the network. How much external drive should be provided to each user, such that the network activity can be steered towards a target state? In this paper, we model social events using multivariate Hawkes processes, which can capture both endogenous and exogenous event intensities, and derive a time dependent linear relation between the intensity of exogenous events and the overall network activity. Exploiting this connection, we develop a convex optimization framework for determining the required level of external drive in order for the network to reach a desired activity level. We experimented with event data gathered from Twitter, and show that our method can steer the activity of the network more accurately than alternatives

    Greedy Maximization Framework for Graph-based Influence Functions

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    The study of graph-based submodular maximization problems was initiated in a seminal work of Kempe, Kleinberg, and Tardos (2003): An {\em influence} function of subsets of nodes is defined by the graph structure and the aim is to find subsets of seed nodes with (approximately) optimal tradeoff of size and influence. Applications include viral marketing, monitoring, and active learning of node labels. This powerful formulation was studied for (generalized) {\em coverage} functions, where the influence of a seed set on a node is the maximum utility of a seed item to the node, and for pairwise {\em utility} based on reachability, distances, or reverse ranks. We define a rich class of influence functions which unifies and extends previous work beyond coverage functions and specific utility functions. We present a meta-algorithm for approximate greedy maximization with strong approximation quality guarantees and worst-case near-linear computation for all functions in our class. Our meta-algorithm generalizes a recent design by Cohen et al (2014) that was specific for distance-based coverage functions.Comment: 8 pages, 1 figur
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