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Influence maximization: Nearoptimal time complexity meets practical efficiency
 in SIGMOD. ACM
, 2014
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Sketchbased influence maximization and computation: Scaling up with guarantees
 In International Conference on Information and Knowledge Management (ICIKM
, 2014
"... Propagation of contagion through networks is a fundamental process. It is used to model the spread of information, influence, or a viral infection. Diffusion patterns can be specified by a probabilistic model, such as Independent Cascade (IC), or captured by a set of representative traces. Basic co ..."
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Propagation of contagion through networks is a fundamental process. It is used to model the spread of information, influence, or a viral infection. Diffusion patterns can be specified by a probabilistic model, such as Independent Cascade (IC), or captured by a set of representative traces. Basic computational problems in the study of diffusion are influence queries (determining the potency of a specified seed set of nodes) and Influence Maximization (identifying the most influential seed set of a given size). Answering each influence query involves many edge traversals, and does not scale when there are many queries on very large graphs. The gold standard for Influence Maximization is the greedy algorithm, which iteratively adds to the seed set a node maximizing the marginal gain in influence. Greedy has a guaranteed approximation ratio of at least (1 − 1/e) and actually produces a sequence of nodes, with each prefix having approximation guarantee with respect to the samesize optimum. Since Greedy does not scale well beyond a few million edges, for larger inputs one must currently use either heuristics or alternative algorithms designed for a prespecified small seed set size. We develop a novel sketchbased design for influence computation. Our greedy Sketchbased Influence Maximization (SKIM) algorithm scales to graphs with billions of edges, with one to two orders of magnitude speedup over the best greedy methods. It still has a guaranteed approximation ratio, and in practice its quality nearly matches that of exact greedy. We also present influence oracles, which use lineartime preprocessing to generate a small sketch for each node, allowing the influence of any seed set to be quickly answered from the sketches of its nodes. 1
Optimal Budget Allocation: Theoretical Guarantee and Efficient Algorithm
, 2014
"... We consider the budget allocation problem over bipartite influence model proposed by Alon et al. (Alon et al., 2012). This problem can be viewed as the wellknown influence maximization problem with budget constraints. We first show that this problem and its much more general form fall into a genera ..."
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We consider the budget allocation problem over bipartite influence model proposed by Alon et al. (Alon et al., 2012). This problem can be viewed as the wellknown influence maximization problem with budget constraints. We first show that this problem and its much more general form fall into a general setting; namely the monotone submodular function maximization over integer lattice subject to a knapsack constraint. Our framework includes Alon et al.’s model, even with a competitor and with cost. We then give a (1 − 1/e)approximation algorithm for this more general problem. Furthermore, when influence probabili
Fast and accurate influence maximization on large networks with pruned montecarlo simulations
 In Conference on Artificial Intelligence (AAAI
, 2014
"... Influence maximization is a problem to find small sets of highly influential individuals in a social network to maximize the spread of influence under stochastic cascade models of propagation. Although the problem has been wellstudied, it is still highly challenging to find solutions of high qualit ..."
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Influence maximization is a problem to find small sets of highly influential individuals in a social network to maximize the spread of influence under stochastic cascade models of propagation. Although the problem has been wellstudied, it is still highly challenging to find solutions of high quality in largescale networks of the day. While MonteCarlosimulationbased methods produce nearoptimal solutions with a theoretical guarantee, they are prohibitively slow for large graphs. As a result, many heuristic methods without any theoretical guarantee have been developed, but all of them substantially compromise solution quality. To address this issue, we propose a new method for the influence maximization problem. Unlike other recent heuristic methods, the proposed method is a MonteCarlosimulationbased method, and thus it consistently produces solutions of high quality with the theoretical guarantee. On the other hand, unlike other previous MonteCarlosimulationbased methods, it runs as fast as other stateoftheart methods, and can be applied to large networks of the day. Through our extensive experiments, we demonstrate the scalability and the solution quality of the proposed method.
Scalable Methods for Adaptively Seeding a Social Network
"... In recent years, social networking platforms have developed into extraordinary channels for spreading and consuming information. Along with the rise of such infrastructure, there is continuous progress on techniques for spreading information effectively through influential users. In many applicat ..."
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In recent years, social networking platforms have developed into extraordinary channels for spreading and consuming information. Along with the rise of such infrastructure, there is continuous progress on techniques for spreading information effectively through influential users. In many applications, one is restricted to select influencers from a set of users who engaged with the topic being promoted, and due to the structure of social networks, these users often rank low in terms of their influence potential. An alternative approach one can consider is an adaptive method which selects users in a manner which targets their influential neighbors. The advantage of such an approach is that it leverages the friendship paradox in social networks: while users are often not influential, they often know someone who is. Despite the various complexities in such optimization problems, we show that scalable adaptive seeding is achievable. In particular, we develop algorithms for linear influence models with provable approximation guarantees that can be gracefully parallelized. To show the effectiveness of our methods we collected data from various verticals social network users follow. For each vertical, we collected data on the users who responded to a certain post as well as their neighbors, and applied our methods on this data. Our experiments show that adaptive seeding is scalable, and importantly, that it obtains dramatic improvements over standard approaches of information dissemination.
Influence at Scale: Distributed Computation of Complex Contagion in Networks
"... We consider the task of evaluating the spread of influence in large networks in the wellstudied independent cascade model. We describe a novel sampling approach that can be used to design scalable algorithms with provable performance guarantees. These algorithms can be implemented in distributed c ..."
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We consider the task of evaluating the spread of influence in large networks in the wellstudied independent cascade model. We describe a novel sampling approach that can be used to design scalable algorithms with provable performance guarantees. These algorithms can be implemented in distributed computation frameworks such as MapReduce. We complement these results with a lower bound on the query complexity of influence estimation in this model. We validate the performance of these algorithms through experiments that demonstrate the efficacy of our methods and related heuristics. 1.
Approximability of Adaptive Seeding under Knapsack Constraints
, 2015
"... Adapting Seeding is a key algorithmic challenge of influence maximization in social networks. One seeks to select among certain available nodes in a network, and then, adaptively, among neighbors of those nodes as they become available, in order to maximize influence in the overall network. Despite ..."
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Adapting Seeding is a key algorithmic challenge of influence maximization in social networks. One seeks to select among certain available nodes in a network, and then, adaptively, among neighbors of those nodes as they become available, in order to maximize influence in the overall network. Despite recent strong approximation results [25, 1], very little is known about the problem when nodes can take on different activation costs. Surprisingly, designing adaptive seeding algorithms that can appropriately incentivize users with heterogeneous activation costs introduces fundamental challenges that do not exist in the simplified version of the problem. In this paper we study the approximability of adaptive seeding algorithms that incentivize nodes with heterogeneous activation costs. We first show a tight inapproximability result which applies even for a very restricted version of the problem. We then complement this inapproximability with a constantfactor approximation for general submodular functions, showing that the difficulties caused by the stochastic nature of the problem can be overcome. In addition, we show stronger approximation results for additive influence functions and cases where the nodes’ activation costs constitute a small fraction of the budget.
Online TopicAware Influence Maximization
"... Influence maximization, whose objective is to select k users (called seeds) from a social network such that the number of users influenced by the seeds (called influence spread) is maximized, has attracted significant attention due to its widespread applications, such as viral marketing and rumor c ..."
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Influence maximization, whose objective is to select k users (called seeds) from a social network such that the number of users influenced by the seeds (called influence spread) is maximized, has attracted significant attention due to its widespread applications, such as viral marketing and rumor control. However, in realworld social networks, users have their own interests (which can be represented as topics) and are more likely to be influenced by their friends (or friends ’ friends) with similar topics. We can increase the influence spread by taking into consideration topics. To address this problem, we study topicaware influence maximization, which, given a topicaware influence maximization (TIM) query, finds k seeds from a social network such that the topicaware influence spread of the k seeds is maximized. Our goal is to enable online TIM queries. Since the topicaware influence maximization problem is NPhard, we focus on devising efficient algorithms to achieve instant performance while keeping a high influence spread. We utilize a maximum influence arborescence (MIA) model to approximate the computation of influence spread. To efficiently find k seeds under the MIA model, we first propose a besteffort algorithm with 1 − 1 e approximation ratio, which estimates an upper bound of the topicaware influence of each user and utilizes the bound to prune large numbers of users with small influence. We devise effective techniques to estimate tighter upper bounds. We then propose a faster topicsamplebased algorithm with · (1 − 1 e) approximation ratio for any ∈ (0, 1], which materializes the influence spread of some topicdistribution samples and utilizes the materialized information to avoid computing the actual influence of users with small influences. Experimental results show that our methods significantly outperform baseline approaches. 1.