This paper studies the fair influence maximization problem with efficient algorithms. In particular, given a graph G, a community structure C consisting of disjoint communities, and a budget k, the problem asks to select a seed set S (|S| = k) that maximizes the influence spread while narrowing the influence gap between different communities. This problem derives from some significant social scenarios, such as health interventions (e.g. suicide/HIV prevention) where individuals from racial minorities or LGBTQ communities may be disproportionately excluded from the benefits of the intervention. To depict the concept of fairness in the context of influence maximization, researchers have proposed various notions of fairness, where the welfare fairness notion that better balances fairness level and influence spread has shown promising effectiveness. However, the lack of efficient algorithms for optimizing the objective function under welfare fairness restricts its application to networks of only a few hundred nodes. In this paper, we modify the objective function of welfare fairness to maximize the exponentially weighted sum and the logarithmically weighted sum over all communities' influenced fractions (utility). To achieve efficient algorithms with theoretical guarantees, we first introduce two unbiased estimators: one for the fractional power of the arithmetic mean and the other for the logarithm of the arithmetic mean. Then, by adapting the Reverse Influence Sampling (RIS) approach, we convert the optimization problem to a weighted maximum coverage problem. We also analyze the number of reverse reachable sets needed to approximate the fair influence at a high probability. Finally, we present an efficient algorithm that guarantees 1 − 1/e − ϵ (positive objective function) or 1 + 1/e + ϵ (negative objective function) approximation for any small ϵ > 0. Experiments demonstrate that our proposed algorithm could efficiently handle large-scale networks with good performance.

In this paper, we study the adversarial attacks on influence maximization under dynamic influence propagation models in social networks. In particular, given a known seed set S, the problem is to minimize the influence spread from S by deleting a limited number of nodes and edges. This problem reflects many application scenarios, such as blocking virus (e.g. COVID-19) propagation in social networks by quarantine and vaccination, blocking rumor spread by freezing fake accounts, or attacking competitor's influence by incentivizing some users to ignore the information from the competitor. In this paper, under the linear threshold model, we adapt the reverse influence sampling approach and provide efficient algorithms of sampling valid reverse reachable paths to solve the problem. We present three different design choices on reverse sampling, which all guarantee 1/2 - ε approximation (for any small ε >0) and an efficient running time.

While social networks greatly facilitate information dissemination, they are well known to have contributed to the phenomena of filter bubbles and echo chambers. This in turn can lead to societal polarization and erosion of trust in public institutions. Mitigating filter bubbles is an urgent open problem. Recently, approaches based on the influence maximization paradigm have been proposed in our community for mitigating filter bubbles by balancing exposure to opposing viewpoints. However, existing works ignore the inherent competition between the adoption of opposing viewpoints by users. In this paper, we propose a realistic model for the filter bubble problem, which unlike previous work, captures thecompetition between opposing opinions propagating in a network as well as thecomplementary nature of the reward forexposing users to both those opinions. We formulate an optimization problem for mitigating filter bubbles under our model. We establish several evidences of the intrinsic difficulty in developing constant approximation to the problem and develop a heuristic and two instance-dependent approximation algorithms. Our experiments over 4 real datasets show that our heuristic far outperforms two state-of-the-art baselines as well as other algorithms in both efficiency and mitigating filter bubbles. We also empirically demonstrate that our best heuristic performs close to the optimal objective, which is obtained by utilizing the theoretical bounds of our approximation algorithms.

In this paper, we present an algorithmic study on how to surpass competitors in popularity by strategic promotions in social networks. We first propose a novel model, in which we integrate the Preferential Attachment (PA) model for popularity growth with the Independent Cascade (IC) model for influence propagation in social networks called PA-IC model. In PA-IC, a popular item and a novice item grab shares of popularity from the natural popularity growth via the PA model, while the novice item tries to gain extra popularity via influence cascade in a social network. The popularity ratio is defined as the ratio of the popularity measure between the novice item and the popular item. We formulate Popularity Ratio Maximization (PRM) as the problem of selecting seeds in multiple rounds to maximize the popularity ratio in the end. We analyze the popularity ratio and show that it is monotone but not submodular. To provide an effective solution, we devise a surrogate objective function and show that empirically it is very close to the original objective function while theoretically, it is monotone and submodular. We design two efficient algorithms, one for the overlapping influence and non-overlapping seeds (across rounds) setting and the other for the non-overlapping influence and overlapping seed setting, and further discuss how to deal with other models and problem variants. Our empirical evaluation further demonstrates that our proposed method consistently achieves the best popularity promotion compared to other methods. Our theoretical and empirical analyses shed light on the interplay between influence maximization and preferential attachment in social networks.

We incorporate the realistic scenario of spontaneous user adoption into influence propagation (also refer to as self-activation) and propose the self-activation independent cascade (SAIC) model: nodes may be self activated besides being selected as seeds, and influence propagates from both selected seeds and self activated nodes. Self activation occurs in many real world situations; for example, people naturally share product recommendations with their friends, even without marketing intervention. Under the SAIC model, we study three influence maximization problems: (a) boosted influence maximization (BIM) aims to maximize the total influence spread from both self-activated nodes and k selected seeds; (b) preemptive influence maximization (PIM) aims to find k nodes that, if self-activated, can reach the most number of nodes before other self-activated nodes; and (c) boosted preemptive influence maximization (BPIM) aims to select k seed that are guaranteed to be activated and can reach the most number of nodes before other self-activated nodes. We propose scalable algorithms for all three problems and prove that they achieve $1-1/e-\varepsilon$ approximation for BIM and BPIM and $1-\varepsilon$ for PIM, for any $\varepsilon > 0$. Through extensive tests on real-world graphs, we demonstrate that our algorithms outperform the baseline algorithms significantly for the PIM problem in solution quality, and also outperform the baselines for BIM and BPIM when self-activation behaviors are nonuniform across nodes.

In this paper, we study the problem of online influence maximization in social networks. In this problem, a learner aims to identify the set of "best influencers" in a network by interacting with the network, i.e., repeatedly selecting seed nodes and observing activation feedback in the network. We capitalize on an important property of the influence maximization problem named network assortativity, which is ignored by most existing works in online influence maximization. To realize network assortativity, we factorize the activation probability on the edges into latent factors on the corresponding nodes, including influence factor on the giving nodes and susceptibility factor on the receiving nodes. We propose an upper confidence bound based online learning solution to estimate the latent factors, and therefore the activation probabilities. Considerable regret reduction is achieved by our factorization based online influence maximization algorithm. Extensive empirical evaluations on two real-world networks showed the effectiveness of our proposed solution.

Motivated by applications such as viral marketing, the problem of influence maximization (IM) has been extensively studied in the literature. The goal is to select a small number of users to adopt an item such that it results in a large cascade of adoptions by others. Existing works have three key limitations. (1) They do not account for economic considerations of a user in buying/adopting items. (2) Most studies on multiple items focus on competition, with complementary items receiving limited attention. (3) For the network owner, maximizing social welfare is important to ensure customer loyalty, which is not addressed in prior work in the IM literature. In this paper, we address all three limitations and propose a novel model called UIC that combines utility-driven item adoption with influence propagation over networks. Focusing on the mutually complementary setting, we formulate the problem of social welfare maximization in this novel setting. We show that while the objective function is neither submodular nor supermodular, surprisingly a simple greedy allocation algorithm achieves a factor of (1-1/e-ε) of the optimum expected social welfare. We develop bundleGRD, a scalable version of this approximation algorithm, and demonstrate, with comprehensive experiments on real and synthetic datasets, that it significantly outperforms all baselines.

In this paper, we study the Multi-Round Influence Maximization (MRIM) problem, where influence propagates in multiple rounds independently from possibly different seed sets, and the goal is to select seeds for each round to maximize the expected number of nodes that are activated in at least one round. MRIM problem models the viral marketing scenarios in which advertisers conduct multiple rounds of viral marketing to promote one product. We consider two different settings: 1) the non-adaptive MRIM, where the advertiser needs to determine the seed sets for all rounds at the very beginning, and 2) the adaptive MRIM, where the advertiser can select seed sets adaptively based on the propagation results in the previous rounds. For the non-adaptive setting, we design two algorithms that exhibit an interesting tradeoff between efficiency and effectiveness: a cross-round greedy algorithm that selects seeds at a global level and achieves $1/2 - \varepsilon$ approximation ratio, and a within-round greedy algorithm that selects seeds round by round and achieves $1-e^-(1-1/e) -\varepsilon \approx 0.46 - \varepsilon$ approximation ratio but saves running time by a factor related to the number of rounds. For the adaptive setting, we design an adaptive algorithm that guarantees $1-e^-(1-1/e) -\varepsilon$ approximation to the adaptive optimal solution. In all cases, we further design scalable algorithms based on the reverse influence sampling approach and achieve near-linear running time. We conduct experiments on several real-world networks and demonstrate that our algorithms are effective for the MRIM task.

The majority of influence maximization (IM) studies focus on targeting influential seeders to trigger substantial information spread in social networks. In this paper, we consider a new and complementary problem of how to further increase the influence spread of given seeders. Our study is motivated by the observation that direct incentives could "boost" users so that they are more likely to be influenced by friends. We study the k-boosting problem which aims to find k users to boost so that the final "boosted" influence spread is maximized. The k-boosting problem is different from the IM problem because boosted users behave differently from seeders: boosted users are initially uninfluenced and we only increase their probability to be influenced. Our work also complements the IM studies because we focus on triggering larger influence spread on the basis of given seeders. Both the NP-hardness of the problem and the non-submodularity of the objective function pose challenges to the k-boosting problem. To tackle the problem, we devise two efficient algorithms with the data-dependent approximation ratio. We conduct extensive experiments using real social networks demonstrating the efficiency and effectiveness of our proposed algorithms. We show that boosting solutions returned by our algorithms achieves boosts of influence that are up to several times higher than those achieved by boosting solutions returned by intuitive baselines, which have no guarantee of solution quality. We also explore the "budget allocation" problem in our experiments. Compared with targeting seeders with all budget, larger influence spread is achieved when we allocation the budget to both seeders and boosted users. This also shows that our study complements the IM studies.

We study network centrality based on dynamic influence propagation models in social networks. To illustrate our integrated mathematical-algorithmic approach for understanding the fundamental interplay between dynamic influence processes and static network structures, we focus on two basic centrality measures: (a) Single Node Influence (SNI) centrality, which measures each node's significance by its influence spread; and (b) Shapley Centrality, which uses the Shapley value of the influence spread function --- formulated based on a fundamental cooperative-game-theoretical concept --- to measure the significance of nodes. We present a comprehensive comparative study of these two centrality measures. Mathematically, we present axiomatic characterizations, which precisely capture the essence of these two centrality measures and their fundamental differences. Algorithmically, we provide scalable algorithms for approximating them for a large family of social-influence instances. Empirically, we demonstrate their similarity and differences in a number of real-world social networks, as well as the efficiency of our scalable algorithms. Our results shed light on their applicability: SNI centrality is suitable for assessing individual influence in isolation while Shapley centrality assesses individuals' performance in group influence settings.

Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component connecting a large portion of the network would emerge. Assessing the percolation threshold of networks has wide applications in network reliability, information spread, epidemic control, etc. The theoretical approach so far to assess the percolation threshold is mainly based on spectral radius of adjacency matrix or non-backtracking matrix, which is limited to dense graphs or locally treelike graphs, and is less effective for sparse networks with non-negligible amount of triangles and loops. In this paper, we study high-order non-backtracking matrices and their application to assessing percolation threshold. We first define high-order non-backtracking matrices and study the properties of their spectral radii. Then we focus on the 2nd-order non-backtracking matrix and demonstrate analytically that the reciprocal of its spectral radius gives a tighter lower bound than those of adjacency and standard non-backtracking matrices. We further build a smaller size matrix with the same largest eigenvalue as the 2nd-order non-backtracking matrix to improve computation efficiency. Finally, we use both synthetic networks and 42 real networks to illustrate that the use of the 2nd-order non-backtracking matrix does give better lower bound for assessing percolation threshold than adjacency and standard non-backtracking matrices.

In this paper, we address the important issue of uncertainty in the edge influence probability estimates for the well studied influence maximization problem --- the task of finding k seed nodes in a social network to maximize the influence spread. We propose the problem of robust influence maximization, which maximizes the worst-case ratio between the influence spread of the chosen seed set and the optimal seed set, given the uncertainty of the parameter input. We design an algorithm that solves this problem with a solution-dependent bound. We further study uniform sampling and adaptive sampling methods to effectively reduce the uncertainty on parameters and improve the robustness of the influence maximization task. Our empirical results show that parameter uncertainty may greatly affect influence maximization performance and prior studies that learned influence probabilities could lead to poor performance in robust influence maximization due to relatively large uncertainty in parameter estimates, and information cascade based adaptive sampling method may be an effective way to improve the robustness of influence maximization.

Kleinberg proposed a family of small-world networks to explain the navigability of large-scale real-world social networks. However, the underlying mechanism that drives real networks to be navigable is not yet well understood. In this paper, we present a game theoretic model for the formation of navigable small world networks. We model the network formation as a game in which people seek for both high reciprocity and long-distance relationships. We show that the navigable small-world network is a Nash Equilibrium of the game. Moreover, we prove that the navigable small-world equilibrium tolerates collusions of any size and arbitrary deviations of a large random set of nodes, while non-navigable equilibria do not tolerate small group collusions or random perturbations. Our empirical evaluation further demonstrates that the system always converges to the navigable network even when limited or no information about other players' strategies is available. Our theoretical and empirical analyses provide important new insight on the connection between distance, reciprocity and navigability in social networks.

Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization , in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation" strategy. The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines on four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.

When a “following” link is formed in a social network, will the link trigger the formation of other neighboring links? We study the diffusion phenomenon of the formation of “following” links by proposing a model to describe this link diffusion process. To estimate the diffusion strength between different links, we first conduct an analysis on the diffusion effect in 24 triadic structures and find evident patterns that facilitate the effect. We then learn the diffusion strength in different triadic structures by maximizing an objective function based on the proposed model. The learned diffusion strength is evaluated through the task of link prediction and utilized to improve the applications of follower maximization and followee recommendation, which are specific instances of influence maximization. Our experimental results reveal that incorporating diffusion patterns can indeed lead to statistically significant improvements over the performance of several alternative methods, which demonstrates the effect of the discovered patterns and diffusion model.

A topic propagating in a social network reaches its tipping point if the number of users discussing it in the network exceeds a critical threshold such that a wide cascade on the topic is likely to occur. In this paper, we consider the task of selecting initial seed users of a topic with minimum size so that {\em with a guaranteed probability} the number of users discussing the topic would reach a given threshold. We formulate the task as an optimization problem called {\em seed minimization with probabilistic coverage guarantee (SM-PCG)}. This problem departs from the previous studies on social influence maximization or seed minimization because it considers influence coverage with {\em probabilistic} guarantees instead of guarantees on {\em expected} influence coverage. We show that the problem is not submodular, and thus is harder than previously studied problems based on submodular function optimization. We provide an approximation algorithm and show that it approximates the optimal solution with both a multiplicative ratio and an additive error. The multiplicative ratio is tight while the additive error would be small if influence coverage distributions of certain seed sets are well concentrated. For one-way bipartite graphs we analytically prove the concentration condition and obtain an approximation algorithm with an $O(\log n)$ multiplicative ratio and an $O(\sqrt{n})$ additive error, where $n$ is the total number of nodes in the social graph. Moreover, we empirically verify the concentration condition in real-world networks and experimentally demonstrate the effectiveness of our proposed algorithm comparing to commonly adopted benchmark algorithms.

Influence maximization, fundamental for word-of-mouth marketing and viral marketing, aims to find a set of seed nodes maximizing influence spread on social network. Early methods mainly fall into two paradigms with certain benefits and drawbacks: (1) Greedy algorithms, selecting seed nodes one by one, give a guaranteed accuracy relying on the accurate approximation of influence spread with high computational cost; (2) Heuristic algorithms, estimating influence spread using efficient heuristics, have low computational cost but unstable accuracy. We first point out that greedy algorithms are essentially finding a self-consistent ranking, where nodes' ranks are consistent with their ranking-based marginal influence spread. This insight motivates us to develop an iterative ranking framework, i.e., IMRank, to efficiently solve influence maximization problem under independent cascade model. Starting from an initial ranking, e.g., one obtained from efficient heuristic algorithm, IMRank finds a self-consistent ranking by reordering nodes iteratively in terms of their ranking-based marginal influence spread computed according to current ranking. We also prove that IMRank definitely converges to a self-consistent ranking starting from any initial ranking. Furthermore, within this framework, a last-to-first allocating strategy and a generalization of this strategy are proposed to improve the efficiency of estimating ranking-based marginal influence spread for a given ranking. In this way, IMRank achieves both remarkable efficiency and high accuracy by leveraging simultaneously the benefits of greedy algorithms and heuristic algorithms. As demonstrated by extensive experiments on large scale real-world social networks, IMRank always achieves high accuracy comparable to greedy algorithms, while the computational cost is reduced dramatically, about 10-100 times faster than other scalable heuristics.

No abstract available.

The problem of identifying rumors is of practical importance especially in online social networks, since information can diffuse more rapidly and widely than the offline counterpart. In this paper, we identify characteristics of rumors by examining the following three aspects of diffusion: temporal, structural, and linguistic. For the temporal characteristics, we propose a new periodic time series model that considers daily and external shock cycles, where the model demonstrates that rumor likely have fluctuations over time. We also identify key structural and linguistic differences in the spread of rumors and non-rumors. Our selected features classify rumors with high precision and recall in the range of 87% to 92%, that is higher than other states of the arts on rumor classification.

Friending recommendation has successfully contributed to the explosive growth of online social networks. Most friending recommendation services today aim to support passive friending, where a user passively selects friending targets from the recommended candidates. In this paper, we advocate a recommendation support for active friending, where a user actively specifies a friending target. To the best of our knowledge, a recommendation designed to provide guidance for a user to systematically approach his friending target has not been explored for existing online social networking services. To maximize the probability that the friending target would accept an invitation from the user, we formulate a new optimization problem, namely, Acceptance Probability Maximization (APM), and develop a polynomial time algorithm, called Selective Invitation with Tree and In-Node Aggregation (SITINA), to find the optimal solution. We implement an active friending service with SITINA on Facebook to validate our idea. Our user study and experimental results reveal that SITINA outperforms manual selection and the baseline approach in solution quality efficiently.

Online social networks become a bridge to connect our physical daily life and the virtual Web space, which not only provides rich data for mining, but also brings many new challenges. In this paper, we present a novel Social Analytic Engine (SAE) for large online social networks. The key issues we pursue in the analytic engine are concerned with the following problems: 1) at the micro-level, how do people form different types of social ties and how people influence each other? 2) at the meso-level, how do people group into communities? 3) at the macro-level, what are the hottest topics in a social network and how the topics evolve over time?

Influence diffusion and influence maximization in large-scale online social networks (OSNs) have been extensively studied because of their impacts on enabling effective online viral marketing. Existing studies focus on social networks with only friendship relations, whereas the foe or enemy relations that commonly exist in many OSNs, e.g., Epinions and Slashdot, are completely ignored. In this paper, we make the first attempt to investigate the influence diffusion and influence maximization in OSNs with both friend and foe relations, which are modeled using positive and negative edges on signed networks. In particular, we extend the classic voter model to signed networks and analyze the dynamics of influence diffusion of two opposite opinions. We first provide systematic characterization of both short-term and long-term dynamics of influence diffusion in this model, and illustrate that the steady state behaviors of the dynamics depend on three types of graph structures, which we refer to as balanced graphs, anti-balanced graphs, and strictly unbalanced graphs. We then apply our results to solve the influence maximization problem and develop efficient algorithms to select initial seeds of one opinion that maximize either its short-term influence coverage or long-term steady state influence coverage. Extensive simulation results on both synthetic and real-world networks, such as Epinions and Slashdot, confirm our theoretical analysis on influence diffusion dynamics, and demonstrate that our influence maximization algorithms perform consistently better than other heuristic algorithms.

Influence maximization is the problem of selecting top k seed nodes in a social network to maximize their influence coverage under certain influence diffusion models. In this paper, we propose a novel algorithm IRIE that integrates the advantages of influence ranking (IR) and influence estimation (IE) methods for influence maximization in both the independent cascade (IC) model and its extension IC-N that incorporates negative opinion propagations. Through extensive experiments, we demonstrate that IRIE matches the influence coverage of other algorithms while scales much better than all other algorithms. Moreover IRIE is much more robust and stable than other algorithms both in running time and memory usage for various density of networks and cascade size. It runs up to two orders of magnitude faster than other state-of-the-art algorithms such as PMIA for large networks with tens of millions of nodes and edges, while using only a fraction of memory.

In many real-world situations, different and often opposite opinions, innovations, or products are competing with one another for their social influence in a networked society. In this paper, we study competitive influence propagation in social networks under the competitive linear threshold (CLT) model, an extension to the classic linear threshold model. Under the CLT model, we focus on the problem that one entity tries to block the influence propagation of its competing entity as much as possible by strategically selecting a number of seed nodes that could initiate its own influence propagation. We call this problem the influence blocking maximization (IBM) problem. We prove that the objective function of IBM in the CLT model is submodular, and thus a greedy algorithm could achieve 1 — 1/e approximation ratio. However, the greedy algorithm requires Monte-Carlo simulations of competitive influence propagation, which makes the algorithm not efficient. We design an efficient algorithm CLDAG, which utilizes the properties of the CLT model, to address this issue. We conduct extensive simulations of CLDAG, the greedy algorithm, and other baseline algorithms on real-world and synthetic datasets. Our results show that CLDAG is able to provide best accuracy in par with the greedy algorithm and often better than other algorithms, while it is two orders of magnitude faster than the greedy algorithm.

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. In this paper, we propose an extension to the independent cascade model that incorporates the emergence and propagation of negative opinions. The new model has an explicit parameter called quality factor to model the natural behavior of people turning negative to a product due to product defects. Our model incorporates negativity bias (negative opinions usually dominate over positive opinions) commonly acknowledged in the social psychology literature. The model maintains some nice properties such as submodularity, which allows a greedy approximation algorithm for maximizing positive influence within a ratio of 1 – 1/e. We define a quality sensitivity ratio (qs-ratio) of influence graphs and show a tight bound of on the qs-ratio, where n is the number of nodes in the network and k is the number of seeds selected, which indicates that seed selection is sensitive to the quality factor for general graphs. We design an efficient algorithm to compute influence in tree structures, which is nontrivial due to the negativity bias in the model. We use this algorithm as the core to build a heuristic algorithm for influence maximization for general graphs. Through simulations, we show that our heuristic algorithm has matching influence with a standard greedy approximation algorithm while being orders of magnitude faster.

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 Kempe et al. 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, 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 Kempe et al. (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.

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.