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Limiting the Spread of Misinformation in Social Networks
"... In this work, we study the notion of competing campaigns in a social network. By modeling the spread of influence in the presence of competing campaigns, we provide necessary tools for applications such as emergency response where the goal is to limit the spread of misinformation. We study the probl ..."
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Cited by 54 (2 self)
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In this work, we study the notion of competing campaigns in a social network. By modeling the spread of influence in the presence of competing campaigns, we provide necessary tools for applications such as emergency response where the goal is to limit the spread of misinformation. We study the problem of influence limitation where a “bad ” campaign starts propagating from a certain node in the network and use the notion of limiting campaigns to counteract the effect of misinformation. The problem can be summarized as identifying a subset of individuals that need to be convinced to adopt the competing (or “good”) campaign so as to minimize the number of people that adopt the “bad ” campaign at the end of both propagation processes. We show that this optimization problem is NPhard and provide approximation guarantees for a greedy solution for various definitions of this problem by proving that they are submodular. Although the greedy algorithm is a polynomial time algorithm, for today’s large scale social networks even this solution is computationally very expensive. Therefore, we study the performance of the degree centrality heuristic as well as other heuristics that have implications on our specific problem. The experiments on a number of closeknit regional networks obtained from the Facebook social network show that in most cases inexpensive heuristics do in fact compare well with the greedy approach.
Threshold models for competitive influence in social networks
 Internet and Network Economics, volume 6484 of Lecture Notes in Computer Science
, 2010
"... The problem of influence maximization deals with choosing the optimal set of nodes in a social network so as to maximize the resulting spread of a technology (opinion, productownership, etc.), given a model of diffusion of influence in a network. A natural extension of this would be to introduce a c ..."
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Cited by 37 (2 self)
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The problem of influence maximization deals with choosing the optimal set of nodes in a social network so as to maximize the resulting spread of a technology (opinion, productownership, etc.), given a model of diffusion of influence in a network. A natural extension of this would be to introduce a competitive setting, in which the goal is to maximize the spread of our technology in the presence of one or more competitors. We suggest several natural extensions to the wellstudied linearthreshold model that was used in the singletechnology case, and show that the original greedy approach cannot be used. Furthermore, we show that for a broad family of competitive influence models, it is NPhard to achieve an approximation that is better than a square root of the optimal solution. Also, we show that the same proof of hardness of approximation can also be applied to give a negative result for a conjecture in [2] about a general cascade model for competitive diffusion. Finally, we suggest a natural model that is amenable to the greedy approach. 1
Competitive Contagion in Networks
"... We develop a gametheoretic framework for the study of competition between firms who have budgets to “seed ” the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of adoptions of their product through a competitive stochasti ..."
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Cited by 36 (2 self)
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We develop a gametheoretic framework for the study of competition between firms who have budgets to “seed ” the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of adoptions of their product through a competitive stochastic diffusion process in the network. This framework yields a rich class of competitive strategies, which depend in subtle ways on the stochastic dynamics of adoption, the relative budgets of the players, and the underlying structure of the social network. We identify a general property of the adoption dynamics — namely, decreasing returns to local adoption — for which the inefficiency of resource use at equilibrium (the Price of Anarchy) is uniformly bounded above, across all networks. We also show that if this property is violated the Price of Anarchy can be unbounded, thus yielding sharp threshold behavior for a broad class of dynamics. We also introduce a new notion, the Budget Multiplier, that measures the extent that imbalances in player budgets can be amplified at equilibrium. We again identify a general property of the adoption dynamics — namely, proportional local adoption between competitors — for which the (pure strategy) Budget Multiplier is uniformly bounded above, across all networks. We show that a violation of this property can lead to unbounded Budget Multiplier, again yielding sharp threshold behavior for a broad class of dynamics.
Word of Mouth: Rumor Dissemination in Social Networks
"... Abstract. In this paper we examine the diffusion of competing rumors in social networks. Two players select a disjoint subset of nodes as initiators of the rumor propagation, seeking to maximize the number of persuaded nodes. We use concepts of game theory and location theory and model the selection ..."
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Cited by 30 (1 self)
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Abstract. In this paper we examine the diffusion of competing rumors in social networks. Two players select a disjoint subset of nodes as initiators of the rumor propagation, seeking to maximize the number of persuaded nodes. We use concepts of game theory and location theory and model the selection of starting nodes for the rumors as a strategic game. We show that computing the optimal strategy for both the first and the second player is NPcomplete, even in a most restricted model. Moreover we prove that determining an approximate solution for the first player is NPcomplete as well. We analyze several heuristics and show that—counterintuitively—being the first to decide is not always an advantage, namely there exist networks where the second player can convince more nodes than the first, regardless of the first player’s decision. 1
Influence Maximization in Social Networks When Negative Opinions May Emerge and Propagate
"... 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 ..."
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Cited by 28 (7 self)
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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. 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 (qsratio) of influence graphs and show a tight bound of Θ ( √ n/k) on the qsratio, 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 Blocking Maximization in Social Networks under the Competitive Linear Threshold Model
"... In many realworld 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) m ..."
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Cited by 25 (5 self)
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In many realworld 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 MonteCarlo 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 realworld 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 in continuous time diffusion networks. arXiv preprint arXiv:1205.1682
, 2012
"... The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the network. However, this still remains largely unexplored to date ..."
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Cited by 24 (6 self)
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The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the network. However, this still remains largely unexplored to date. To this end, given a network and its temporal dynamics, we first describe how continuous time Markov chains allow us to analytically compute the average total number of nodes reached by a diffusion process starting in a set of source nodes. We then show that selecting the set of most influential source nodes in the continuous time influence maximization problem is NPhard and develop an efficient approximation algorithm with provable nearoptimal performance. Experiments on synthetic and real diffusion networks show that our algorithm outperforms other state of the art algorithms by at least ∼20 % and is robust across different network topologies. 1.
Clash of the Contagions: Cooperation and Competition in Information Diffusion
"... Abstract—In networks, contagions such as information, purchasing behaviors, and diseases, spread and diffuse from node to node over the edges of the network. Moreover, in realworld scenarios multiple contagions spread through the network simultaneously. These contagions not only propagate at the sa ..."
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Cited by 23 (3 self)
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Abstract—In networks, contagions such as information, purchasing behaviors, and diseases, spread and diffuse from node to node over the edges of the network. Moreover, in realworld scenarios multiple contagions spread through the network simultaneously. These contagions not only propagate at the same time but they also interact and compete with each other as they spread over the network. While traditional empirical studies and models of diffusion consider individual contagions as independent and thus spreading in isolation, we study how different contagions interact with each other as they spread through the network. We develop a statistical model that allows for competition as well as cooperation of different contagions in information diffusion. Competing contagions decrease each other’s probability of spreading, while cooperating contagions help each other in being adopted throughout the network. We evaluate our model on 18,000 contagions simultaneously spreading through the Twitter network. Our model learns how different contagions interact with each other and then uses these interactions to more accurately predict the diffusion of a contagion through the network. Moreover, the model also provides a compelling hypothesis for the principles that govern content interaction in information diffusion. Most importantly, we find very strong effects of interactions between contagions. Interactions cause a relative change in the spreading probability of a contagion by 71 % on the average. I.
Scalable influence estimation in continuoustime diffusion networks
 In
, 2013
"... If a piece of information is released from a media site, can we predict whether it may spread to one million web pages, in a month? This influence estimation problem is very challenging since both the timesensitive nature of the task and the requirement of scalability need to be addressed simultane ..."
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Cited by 23 (6 self)
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If a piece of information is released from a media site, can we predict whether it may spread to one million web pages, in a month? This influence estimation problem is very challenging since both the timesensitive nature of the task and the requirement of scalability need to be addressed simultaneously. In this paper, we propose a randomized algorithm for influence estimation in continuoustime diffusion networks. Our algorithm can estimate the influence of every node in a network with V  nodes and E  edges to an accuracy of using n = O(1/2) randomizations and up to logarithmic factorsO(nE+nV) computations. When used as a subroutine in a greedy influence maximization approach, our proposed algorithm is guaranteed to find a set of C nodes with the influence of at least (1 − 1/e) OPT−2C, where OPT is the optimal value. Experiments on both synthetic and realworld data show that the proposed algorithm can easily scale up to networks of millions of nodes while significantly improves over previous stateofthearts in terms of the accuracy of the estimated influence and the quality of the selected nodes in maximizing the influence. 1
Bounded budget connection (BBC) games or how to make friends and influence people, on a budget
 in Proceedings of the 27th ACM Symposium on Principles of Distributed Computing
"... Motivated by applications in social networks, peertopeer and overlay networks, we define and study the Bounded Budget Connection (BBC) game we have a collection of n players or nodes each of whom has a budget for purchasing links; each link has a cost as well as a length and each node has a set o ..."
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Cited by 19 (2 self)
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Motivated by applications in social networks, peertopeer and overlay networks, we define and study the Bounded Budget Connection (BBC) game we have a collection of n players or nodes each of whom has a budget for purchasing links; each link has a cost as well as a length and each node has a set of preference weights for each of the remaining nodes; the objective of each node is to use its budget to buy a set of outgoing links so as to minimize its sum of preferenceweighted distances to the remaining nodes. We study the structural and complexitytheoretic properties of pure Nash equilibria in BBC games. We show that determining the existence of a pure Nash equilibrium in general BBC games is NPhard. We counterbalance this result by considering a natural variant, fractional BBC games where it is permitted to buy fractions of links and show that a pure Nash equilibrium always exists in such games. A major focus is the study of (n, k)uniform BBC games those in which all link costs, link lengths and preference weights are equal (to 1) and all budgets are equal (to k). We show that a pure Nash equilibrium or stable graph exists for all (n, k)uniform BBC games and that all stable graphs are essentially fair (i.e. all nodes have similar costs). We provide an explicit construction of a family of stable graphs that spans the spectrum from minimum total social cost to maximum total social cost. To be precise we show that that the price of stability is Θ(1) and the price of anarchy is Ω( n/k) and O( logk n