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87
Efficient influence maximization in social networks
 In Proc. of ACM KDD
, 2009
"... 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 ..."
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Cited by 197 (18 self)
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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 centralitybased 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 finetuned 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.
Competitive influence maximization in social networks
 In WINE
, 2007
"... Abstract. Social networks often serve as a medium for the diffusion of ideas or innovations. An individual’s decision whether to adopt a product or innovation will be highly dependent on the choices made by the individual’s peers or neighbors in the social network. In this work, we study the game of ..."
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Cited by 87 (2 self)
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Abstract. Social networks often serve as a medium for the diffusion of ideas or innovations. An individual’s decision whether to adopt a product or innovation will be highly dependent on the choices made by the individual’s peers or neighbors in the social network. In this work, we study the game of innovation diffusion with multiple competing innovations such as when multiple companies market competing products using viral marketing. Our first contribution is a natural and mathematically tractable model for the diffusion of multiple innovations in a network. We give a (1−1/e) approximation algorithm for computing the best response to an opponent’s strategy, and prove that the “price of competition ” of this game is at most 2. We also discuss “first mover ” strategies which try to maximize the expected diffusion against perfect competition. Finally, we give an FPTAS for the problem of maximizing the influence of a single player when the underlying graph is a tree. 1
Cascading behavior in networks: Algorithmic and economic issues
, 2007
"... The flow of information or influence through a large social network can be thought of as unfolding with the dynamics of an epidemic: as individuals become aware of new ideas, technologies, fads, rumors, or gossip, they have the potential to pass them on to their friends and colleagues, causing the ..."
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Cited by 82 (1 self)
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The flow of information or influence through a large social network can be thought of as unfolding with the dynamics of an epidemic: as individuals become aware of new ideas, technologies, fads, rumors, or gossip, they have the potential to pass them on to their friends and colleagues, causing the resulting behavior to cascade through the network. We consider a collection of probabilistic and gametheoretic models for such phenomena proposed in the mathematical social sciences, as well as recent algorithmic work on the problem by computer scientists. Building on this, we discuss the implications of cascading behavior in a number of online settings, including wordofmouth effects (also known as “viral marketing”) in the success of new products, and the influence of social networks in the growth of online communities. 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.
A Note on Maximizing the Spread of Influence in Social Networks
"... Abstract. We consider the spread maximization problem that was defined by Domingos and Richardson [7, 22]. In this problem, we are given a social network represented as a graph and are required to find the set of the most “influential ” individuals that by introducing them with a new technology, we ..."
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Cited by 35 (0 self)
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Abstract. We consider the spread maximization problem that was defined by Domingos and Richardson [7, 22]. In this problem, we are given a social network represented as a graph and are required to find the set of the most “influential ” individuals that by introducing them with a new technology, we maximize the expected number of individuals in the network, later in time, that adopt the new technology. This problem has applications in viral marketing, where a company may wish to spread the rumor of a new product via the most influential individuals in popular social networks such as Myspace and Blogsphere. The spread maximization problem was recently studied in several models of social networks [14, 15, 20]. In this short paper we study this problem in the context of the well studied probabilistic voter model. We provide very simple and efficient algorithms for solving this problem. An interesting special case of our result is that the most natural heuristic solution, which picks the nodes in the network with the highest degree, is indeed the optimal solution.
Finding Spread Blockers in Dynamic Networks
"... Social interactions are conduits for various processes spreading through a population, from rumors and opinions to behaviors and diseases. In the context of the spread of a disease or undesirable behavior, it is important to identify blockers: individuals that are most effective in stopping or slow ..."
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Cited by 26 (2 self)
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Social interactions are conduits for various processes spreading through a population, from rumors and opinions to behaviors and diseases. In the context of the spread of a disease or undesirable behavior, it is important to identify blockers: individuals that are most effective in stopping or slowing down the spread of a process through the population. This problem has so far resisted systematic algorithmic solutions. In an effort to formulate practical solutions, in this paper we ask: Are there structural network measures that are indicative of the best blockers in dynamic social networks? Our contribution is twofold. First, we extend standard structural network measures to dynamic networks. Second, we compare the blocking ability of individuals in the order of ranking by the new dynamic measures. We found that overall, simple ranking according to a node’s static degree, or the dynamic version of a node’s degree, performed consistently well. Surprisingly the dynamic clustering coefficient seems to be a good indicator, while its static version performs worse than the random ranking. This provides simple practical and locally computable algorithms for identifying key blockers in a network.
Treewidth Governs the Complexity of Target Set Selection
, 2009
"... In this paper we study the Target Set Selection problem proposed by Kempe, Kleinberg, and Tardos; a problem which gives a nice clean combinatorial formulation for many applications arising in economy, sociology, and medicine. Its input is a graph with vertex thresholds, the social network, and the g ..."
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Cited by 25 (0 self)
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In this paper we study the Target Set Selection problem proposed by Kempe, Kleinberg, and Tardos; a problem which gives a nice clean combinatorial formulation for many applications arising in economy, sociology, and medicine. Its input is a graph with vertex thresholds, the social network, and the goal is to find a subset of vertices, the target set, that “activates ” a prespecified number of vertices in the graph. Activation of a vertex is defined via a socalled activation process as follows: Initially, all vertices in the target set become active. Then at each step i of the process, each vertex gets activated if the number of its active neighbors at iteration i−1 exceeds its threshold. The activation process is “monotone ” in the sense that once a vertex is activated, it remains active for the entire process. Our contribution is as follows: First, we present an algorithm for Target Set Selection running in n O(w) time, for graphs with n vertices and treewidth bounded by w. This algorithm can be adopted to much more general settings, including the case of directed graphs, weighted edges, and weighted vertices. On the other hand, we also show that it is highly unlikely to find an n o( √ w) time algorithm for Target Set Selection, as this would imply a subexponential algorithm for all problems in SNP. Together with our upper bound result, this shows that the treewidth parameter determines the complexity of Target Set Selection to a large extent, and should be taken into consideration when tackling this problem in any scenario. In the last part of the paper we also deal with the “nonmonotone” variant of Target Set Selection, and show that this problem becomes #Phard on graphs with edge weights.
How to win friends and influence people, truthfully: Influence maximization mechanisms for social networks
 In WSDM
, 2012
"... Throughout the past decade there has been extensive research on algorithmic and data mining techniques for solving the problem of influence maximization in social networks: if one can incentivize a subset of individuals to become early adopters of a new technology, which subset should be selected so ..."
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Cited by 24 (3 self)
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Throughout the past decade there has been extensive research on algorithmic and data mining techniques for solving the problem of influence maximization in social networks: if one can incentivize a subset of individuals to become early adopters of a new technology, which subset should be selected so that the wordofmouth effect in the social network is maximized? Despite the progress in modeling and techniques, the incomplete information aspect of the problem has been largely overlooked. While data can often provide the network structure and influence patterns may be observable, the inherent cost individuals have to become early adopters is difficult to extract. In this paper we introduce mechanisms that elicit individuals’ costs while providing desirable approximation guarantees in some of the most wellstudied models of social network influence. We follow the mechanism design framework which advocates for allocation and payment schemes that incentivize individuals to report their true information. We also performed experiments using the Mechanical Turk platform and social network data to provide evidence of the framework’s effectiveness in practice.
Sketching Valuation Functions
, 2011
"... Motivated by the problem of querying and communicating bidders ’ valuations in combinatorial auctions, we study how well different classes of set functions can be sketched. More formally, let f be a function mapping subsets of some ground set [n] to the nonnegative real numbers. We say that f ′ is ..."
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Cited by 23 (2 self)
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Motivated by the problem of querying and communicating bidders ’ valuations in combinatorial auctions, we study how well different classes of set functions can be sketched. More formally, let f be a function mapping subsets of some ground set [n] to the nonnegative real numbers. We say that f ′ is an αsketch of f if for every set S, the value f ′ (S) lies between f(S)/α and f(S), and f ′ can be specified by poly(n) bits. We show that for every subadditive function f there exists an αsketch where α = n 1/2 · O(polylog(n)). Furthermore, we provide an algorithm that finds these sketches with a polynomial number of demand queries. This is essentially the best we can hope for since: 1. We show that there exist subadditive functions (in fact, XOS functions) that do not admit an o(n 1/2) sketch. (Balcan and Harvey [3] previously showed that there exist functions belonging to the class of substitutes valuations that do not admit an O(n 1/3) sketch.) 2. We prove that every deterministic algorithm that accesses the function via value queries only cannot guarantee a sketching ratio better than n 1−ɛ. We also show that coverage functions, an interesting subclass of submodular functions, admit arbitrarily good sketches.