Influence maximization (IM) has been extensively studied for better viral marketing. However, previous works put less emphasis on how balancedly the audience are affected across different communities and how diversely the seed nodes are selected. In this paper, we incorporate audience diversity and seed diversity into the IM task. From the model perspective, in order to characterize both influence spread and diversity in our objective function, we adopt three commonly used utilities in economics (i.e., Perfect Substitutes, Perfect Complements and Cobb-Douglas). We validate our choices of these three functions by showing their nice properties. From the algorithmic perspective, we present various approximation strategies to maximize the utilities. In audience diversification, we propose a solution-dependent approximation algorithm to circumvent the hardness results. In seed diversification, we prove a ( @math ) approximation ratio based on non-monotonic submodular maximization. Experimental results show that our framework outperforms other natural heuristics both in utility maximization and result diversification.
@cite_22 first formalize IM as a discrete optimization problem. Subsequent efforts following their framework can be divided into two directions. In one direction, researchers focus on how to accelerate the vanilla hill-climbing greedy algorithm @cite_10 @cite_36 @cite_37 @cite_9 @cite_17 @cite_25 @cite_18 @cite_33 . In the other direction, researchers propose new problem settings @cite_21 @cite_30 @cite_28 @cite_34 @cite_5 based on IM. Due to space limitation, we do not list all the variants here. One can refer to a recent tutorial @cite_40 for more details. Despite their success, the final cascade size is their primary criterion in selecting influential nodes. In contrast, our model incorporates diversity as a factor.
@cite_30 @cite_37 @cite_18 @cite_22 @cite_33 @cite_36 @cite_28 @cite_9 @cite_21 @cite_40 @cite_5 @cite_34 @cite_10 @cite_25 @cite_17
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Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. The scalability of influence maximization is a key factor for enabling prevalent viral marketing in large-scale online social networks. Prior solutions, such as the greedy algorithm of (2003) and its improvements are slow and not scalable, while other heuristic algorithms do not provide consistently good performance on influence spreads. In this paper, we design a new heuristic algorithm that is easily scalable to millions of nodes and edges in our experiments. Our algorithm has a simple tunable parameter for users to control the balance between the running time and the influence spread of the algorithm. Our results from extensive simulations on several real-world and synthetic networks demonstrate that our algorithm is currently the best scalable solution to the influence maximization problem: (a) our algorithm scales beyond million-sized graphs where the greedy algorithm becomes infeasible, and (b) in all size ranges, our algorithm performs consistently well in influence spread --- it is always among the best algorithms, and in most cases it significantly outperforms all other scalable heuristics to as much as 100 --260 increase in influence spread. Given a social network G and a positive integer k, the influence maximization problem asks for k nodes (in G) whose adoptions of a certain idea or product can trigger the largest expected number of follow-up adoptions by the remaining nodes. This problem has been extensively studied in the literature, and the state-of-the-art technique runs in O((k+l) (n+m) log n e2) expected time and returns a (1-1 e-e)-approximate solution with at least 1 - 1 n l probability. This paper presents an influence maximization algorithm that provides the same worst-case guarantees as the state of the art, but offers significantly improved empirical efficiency. The core of our algorithm is a set of estimation techniques based on martingales, a classic statistical tool. Those techniques not only provide accurate results with small computation overheads, but also enable our algorithm to support a larger class of information diffusion models than existing methods do. We experimentally evaluate our algorithm against the states of the art under several popular diffusion models, using real social networks with up to 1.4 billion edges. Our experimental results show that the proposed algorithm consistently outperforms the states of the art in terms of computation efficiency, and is often orders of magnitude faster. Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63 of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks. Influence maximization is a classic and extensively studied problem with important applications in viral marketing. Existing algorithms for influence maximization, however, mostly focus on offline processing, in the sense that they do not provide any output to the user until the final answer is derived, and that the user is not allowed to terminate the algorithm early to trade the quality of solution for efficiency. Such lack of interactiveness and flexibility leads to poor user experience, especially when the algorithm incurs long running time. To address the above problem, this paper studies algorithms for online processing of influence maximization (OPIM), where the user can pause the algorithm at any time and ask for a solution (to the influence maximization problem) and its approximation guarantee, and can resume the algorithm to let it improve the quality of solution by giving it more time to run. (This interactive paradigm is similar in spirit to online query processing in database systems.) We show that the only existing algorithm for OPIM is vastly ineffective in practice, and that adopting existing influence maximization methods for OPIM yields unsatisfactory results. Motivated by this, we propose a new algorithm for OPIM with both superior empirical effectiveness and strong theoretical guarantees, and we show that it can also be extended to handle conventional influence maximization. Extensive experiments on real data demonstrate that our solutions outperform the state of the art for both OPIM and conventional influence maximization. Influence maximization is the problem of finding a small subset of nodes (seed nodes) in a social network that could maximize the spread of influence. In this paper, we study the efficient influence maximization from two complementary directions. One is to improve the original greedy algorithm of [5] and its improvement [7] to further reduce its running time, and the second is to propose new degree discount heuristics that improves influence spread. We evaluate our algorithms by experiments on two large academic collaboration graphs obtained from the online archival database arXiv.org. Our experimental results show that (a) our improved greedy algorithm achieves better running time comparing with the improvement of [7] with matching influence spread, (b) our degree discount heuristics achieve much better influence spread than classic degree and centrality-based heuristics, and when tuned for a specific influence cascade model, it achieves almost matching influence thread with the greedy algorithm, and more importantly (c) the degree discount heuristics run only in milliseconds while even the improved greedy algorithms run in hours in our experiment graphs with a few tens of thousands of nodes. Based on our results, we believe that fine-tuned heuristics may provide truly scalable solutions to the influence maximization problem with satisfying influence spread and blazingly fast running time. Therefore, contrary to what implied by the conclusion of [5] that traditional heuristics are outperformed by the greedy approximation algorithm, our results shed new lights on the research of heuristic algorithms. Influence maximization is the problem of finding a small set of most influential nodes in a social network so that their aggregated influence in the network is maximized. In this paper, we study influence maximization in the linear threshold model, one of the important models formalizing the behavior of influence propagation in social networks. We first show that computing exact influence in general networks in the linear threshold model is #P-hard, which closes an open problem left in the seminal work on influence maximization by Kempe, Kleinberg, and Tardos, 2003. As a contrast, we show that computing influence in directed a cyclic graphs (DAGs) can be done in time linear to the size of the graphs. Based on the fast computation in DAGs, we propose the first scalable influence maximization algorithm tailored for the linear threshold model. We conduct extensive simulations to show that our algorithm is scalable to networks with millions of nodes and edges, is orders of magnitude faster than the greedy approximation algorithm proposed by and its optimized versions, and performs consistently among the best algorithms while other heuristic algorithms not design specifically for the linear threshold model have unstable performances on different real-world networks. Influence maximization is a fundamental research problem in social networks. Viral marketing, one of its applications, is to get a small number of users to adopt a product, which subsequently triggers a large cascade of further adoptions by utilizing """"Word-of-Mouth"""" effect in social networks. Influence maximization problem has been extensively studied recently. However, none of the previous work considers the time constraint in the influence maximization problem. In this paper, we propose the time constrained influence maximization problem. We show that the problem is NP-hard, and prove the monotonicity and submodularity of the time constrained influence spread function. Based on this, we develop a greedy algorithm with performance guarantees. To improve the algorithm scalability, we propose two Influence Spreading Path based methods. Extensive experiments conducted over four public available datasets demonstrate the efficiency and effectiveness of the Influence Spreading Path based methods. Starting with the earliest studies showing that the spread of new trends, information, and innovations is closely related to the social influence exerted on people by their social networks, the research on social influence theory took off, providing remarkable evidence on social influence induced viral phenomena. Fueled by the extreme popularity of online social networks and social media, computational social influence has emerged as a subfield of data mining whose goal is to analyze and optimize social influence using computational frameworks such as algorithm design and theoretical modeling. One of the fundamental problems in this field is the problem of influence maximization, primarily motivated by the application of viral marketing. The objective is to identify a small set of users in a social network who, when convinced to adopt a product, shall influence others in the network in a manner that leads to a large number of adoptions. In this tutorial, we extensively survey the research on social influence propagation and maximization, with a focus on the recent algorithmic and theoretical advances. To this end, we provide detailed reviews of the latest research effort devoted to (i) improving the efficiency and scalability of the influence maximization algorithms; (ii) context-aware modeling of the influence maximization problem to better capture real-world marketing scenarios; (iii) modeling and learning of real-world social influence; (iv) bridging the gap between social advertising and viral marketing. Influence maximization, the fundamental of viral marketing, aims to find top- @math seed nodes maximizing influence spread under certain spreading models. In this paper, we study influence maximization from a game perspective. We propose a Coordination Game model, in which every individuals make their decisions based on the benefit of coordination with their network neighbors, to study information propagation. Our model serves as the generalization of some existing models, such as Majority Vote model and Linear Threshold model. Under the generalized model, we study the hardness of influence maximization and the approximation guarantee of the greedy algorithm. We also combine several strategies to accelerate the algorithm. Experimental results show that after the acceleration, our algorithm significantly outperforms other heuristics, and it is three orders of magnitude faster than the original greedy method. 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 settings. 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 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. Given a water distribution network, where should we place sensors toquickly detect contaminants? Or, which blogs should we read to avoid missing important stories?. These seemingly different problems share common structure: Outbreak detection can be modeled as selecting nodes (sensor locations, blogs) in a network, in order to detect the spreading of a virus or information asquickly as possible. We present a general methodology for near optimal sensor placement in these and related problems. We demonstrate that many realistic outbreak detection objectives (e.g., detection likelihood, population affected) exhibit the property of "submodularity". We exploit submodularity to develop an efficient algorithm that scales to large problems, achieving near optimal placements, while being 700 times faster than a simple greedy algorithm. We also derive online bounds on the quality of the placements obtained by any algorithm. Our algorithms and bounds also handle cases where nodes (sensor locations, blogs) have different costs. We evaluate our approach on several large real-world problems,including a model of a water distribution network from the EPA, andreal blog data. The obtained sensor placements are provably near optimal, providing a constant fraction of the optimal solution. We show that the approach scales, achieving speedups and savings in storage of several orders of magnitude. We also show how the approach leads to deeper insights in both applications, answering multicriteria trade-off, cost-sensitivity and generalization questions. Given a social network G and a constant @math , 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+ l) (n+m) log n e2) expected time and returns a (1-1 e-e)-approximate solution with at least 1 - n-l probability. The time complexity of TIM is near-optimal under the IC model, as it is only a log n factor larger than the Ω(m + n) lower-bound established in previous work (for fixed k, l, and e). 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, e = 0.2, and l = 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. This demonstrates that influence maximization algorithms can be made practical while still offering strong theoretical guarantees. Diffusion is a fundamental graph process, underpinning such phenomena as epidemic disease contagion and the spread of innovation by word-of-mouth. We address the algorithmic problem of finding a set of k initial seed nodes in a network so that the expected size of the resulting cascade is maximized, under the standard independent cascade model of network diffusion. Runtime is a primary consideration for this problem due to the massive size of the relevant input networks. We provide a fast algorithm for the influence maximization problem, obtaining the near-optimal approximation factor of (1--1 e -- e), for any e > 0, in time O((m + n)e-3 log n). Our algorithm is runtime-optimal (up to a logarithmic factor) and substantially improves upon the previously best-known algorithms which run in time Ω(mnk · POLY(e-1)). Furthermore, our algorithm can be modified to allow early termination: if it is terminated after O(β(m + n) log n) steps for some β < 1 (which can depend on n), then it returns a solution with approximation factor O(β). Finally, we show that this runtime is optimal (up to logarithmic factors) for any β and fixed seed size k.