On the submodularity of influence in social networks

Mossel, Elchanan; Roch, Sébastien

doi:10.1145/1250790.1250811

Cited by 186 publications

(160 citation statements)

References 15 publications

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“…Several similar models describing particle interactions have been studied previously, including the SIR and SIS epidemic models [9,Chapter 21], the voter model, the antivoter model and the exclusion process [1,8,21]. Related models, such as the decreasing cascade model [19,25], have been studied in the context of influence propagation in social networks and other models have been considered for dynamic monopolies [3]. However, these models do not consider different fitnesses for the individuals.…”

Section: Introductionmentioning

confidence: 99%

Approximating Fixation Probabilities in the Generalized Moran Process

et al. 2012

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Citation for published item:h¡ % zD tF nd qold ergD vFeF nd wertziosD qFfF nd i her yD hF nd ern D wF nd pir kisD FqF @PHIRA 9epproxim ting (x tion pro ilities in the gener lized wor n pro essF9D elgorithmi FD TW @IAF ppF UVEWIFFurther information on publisher's website:The nal publication is available at Springer via http://dx.doi.org/10.1007/s00453-012-9722-7.Additional information:A preliminary version of this work appeared in Proceedings of the ACM SIAM Symposium on Discrete Algorithms (SODA), pp. 954 960, 2012. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe consider the Moran process, as generalized by Lieberman, Hauert and Nowak (Nature, 433:312-316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at random with probability proportional to its assigned "fitness" value. It reproduces, placing a copy of itself on a neighbouring vertex chosen uniformly at random, replacing the individual that was there. The initial population consists of a single mutant of fitness r > 0 placed uniformly at random, with every other vertex occupied by an individual of fitness 1. The main quantities of interest are the probabilities that the descendants of the initial mutant come to occupy the whole graph (fixation) and that they die out (extinction); almost surely, these are the only possibilities. In general, exact computation of these quantities by standard Markov chain techniques requires solving a system of linear equations of size exponential in the order of the graph so is not feasible. We show that, with high probability, the number of steps needed to reach fixation or extinction is bounded by a polynomial in the number of vertices in the graph. This bound allows us to construct fully polynomial randomized approximation schemes (FPRAS) for the probability of fixation (when r 1) and of extinction (for all r > 0). * A preliminary version of this work appeared in

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Section: Introductionmentioning

confidence: 99%

Approximating Fixation Probabilities in the Generalized Moran Process

et al. 2012

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“…To transfer the randomness of our inherent valuation to the threshold side of the general threshold model, we use the inverse transform method where one simulates a random variable X with distribution function H by using H −1 (U ) where U is uniform in Since Q i,p and f i are non-decreasing and concave, the composition Q i,p (f i (·)) is concave as well and Q i,p (f i ( j∈S w ij )) is submodular in S. Hence, we have shown that for any fixed p, the dynamics of the influence stage are equivalent to a submodular general threshold model. In particular, by the results in [15], we have that h i p is submodular. We finish the proof of Proposition 1 by proving the following lemma.…”

Section: Theorem 1 (Approximation)mentioning

confidence: 78%

“…The canonical question in this literature, first posed by Domingos and Richardson [5], is: Which set I of influential nodes of cardinality k in a social network should be convinced to use a service, so that subsequent adoption of the service is maximized? This literature has made substantial progress in understanding the cascading of process of adoption and using this to optimize for I (see for instance [5,11,12,15]). However, this literature does not model the impact of price on the probabiity of adopting a service and does not attempt to quantify the revenue from adoption.…”

Section: Introductionmentioning

confidence: 99%

On Fixed-Price Marketing for Goods with Positive Network Externalities

Mirrokni

Roch

Sundararajan

2012

Lecture Notes in Computer Science

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Abstract. In this paper we discuss marketing strategies for goods that have positive network externalities, i.e., when a buyer's value for an item is positively influenced by others owning the item. We investigate revenue-optimal strategies of a specific form where the seller gives the item for free to a set of users, and then sets a fixed price for the rest. We present a 1 2 -approximation for this problem under assumptions about the form of the externality. To do so, we apply ideas from the influence maximization literature [13] and also use a recent result on non-negative submodular maximization as a blax-box [3,7].

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“…The problem of identifying influential nodes of a social network in order to incite cascades, introduced by Kempe et al [12] and studied further in [13,15], shares some of the spirit of the optimization problem studied in the present work.…”

Section: Introductionmentioning

confidence: 93%

Preventing Unraveling in Social Networks: The Anchored k-Core Problem

Bhawalkar

Kleinberg

Lewi

et al. 2012

Automata, Languages, and Programming

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Abstract. We consider a model of user engagement in social networks, where each player incurs a cost to remain engaged but derives a benefit proportional to the number of engaged neighbors. The natural equilibrium of this model corresponds to the k-core of the social network -the maximal induced subgraph with minimum degree at least k. We study the problem of "anchoring" a small number of vertices to maximize the size of the corresponding anchored k-core -the maximal induced subgraph in which every non-anchored vertex has degree at least k. This problem corresponds to preventing "unraveling" -a cascade of iterated withdrawals. We provide polynomialtime algorithms for general graphs with k = 2, and for boundedtreewidth graphs with arbitrary k. We prove strong inapproximability results for general graphs and k ≥ 3.

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On the submodularity of influence in social networks

Cited by 186 publications

References 15 publications

Approximating Fixation Probabilities in the Generalized Moran Process

Approximating Fixation Probabilities in the Generalized Moran Process

On Fixed-Price Marketing for Goods with Positive Network Externalities

Preventing Unraveling in Social Networks: The Anchored k-Core Problem

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