Spread of influence in weighted networks under time and budget constraints

Structural Information and Communication Complexity

Peters

et al. 2018

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A widely studied model of influence diffusion in social networks represents the network as a graph G = (V, E) with an influence threshold t(v) for each node. Initially the members of an initial set S ⊆ V are influenced. During each subsequent round, the set of influenced nodes is augmented by including every node v that has at least t(v) previously influenced neighbours. The general problem is to find a small initial set that influences the whole network. In this paper we extend this model by using incentives to reduce the thresholds of some nodes. The goal is to minimize the total of the incentives required to ensure that the process completes within a given number of rounds. The problem is hard to approximate in general networks. We present polynomial-time algorithms for paths, trees, and complete networks.

Section: Related Work and Our Resultsmentioning

confidence: 99%

Section: Related Work and Our Resultsmentioning

confidence: 99%

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Time-Bounded Influence Diffusion with Incentives

Structural Information and Communication Complexity

Peters

et al. 2018

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“…A polynomial-time algorithm for trees was given in the same paper. Chen's inapproximability result stimulated a series of papers (see for instance [1,2,3,6,7,11,12,13,14,15,16,24,25,30,36,39,40,42,44,45] and references therein quoted) that isolated many interesting scenarios in which the problem and variants thereof become tractable. Ben-Zwi et al [3] generalized Chen's result on trees to show that target set selection can be solved in n O(w) time where w is the treewidth of the input graph.…”

Section: Related Workmentioning

confidence: 99%

Whom to befriend to influence people

Theoretical Computer Science

Lafond

et al. 2020

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Alice wants to join a new social network, and influence its members to adopt a new product or idea. Each person v in the network has a certain threshold t(v) for activation, i.e adoption of the product or idea. If v has at least t(v) activated neighbors, then v will also become activated. If Alice wants to activate the entire social network, whom should she befriend? More generally, we study the problem of finding the minimum number of links that a set of external influencers should form to people in the network, in order to activate the entire social network. This Minimum Links Problem has applications in viral marketing and the study of epidemics. Its solution can be quite different from the related and widely studied Target Set Selection problem. We prove that the Minimum Links problem cannot be approximated to within a ratio of O(2 log 1−ε n ), for any fixed ε > 0, unless NP ⊆ DT IME(n polylog(n) ), where n is the number of nodes in the network. On the positive side, we give linear time algorithms to solve the problem for trees, cycles, and cliques, for any given set of external influencers, and give precise bounds on the number of links needed. For general graphs, we design a polynomial time algorithm to compute size-efficient link sets that can activate the entire graph.1 G = (V, E,t) with V (G) representing individuals in the social network, E(G) denoting the social connections, and t an integer-valued threshold function. Starting with a target set, that is, a subset S ⊆ V of nodes in the graph, that are activated by some external incentive, influence propagates deterministically in discrete time steps, and activates nodes.For any unactivated node v, if the number of its activated neighbors at time step t − 1 is at least t(v), then node v will be activated in step t. A node once activated stays activated. It is easy to see that if S is non-empty, then the process terminates after at most |V | − 1 steps. We call the set of nodes that are activated when the process terminates as the activated set. The problem proposed by Domingo and Richardson [21,43] can now be formulated as follows: Given a social network G = (V, E,t), and an integer k, find a subset S ⊆ V of size k so that the resulting activated set is as large as possible. In the context of viral marketing, the parameter k corresponds to the budget, and S is a target set that maximizes the size of the activated set. One question of interest is to find the cheapest way to activate the entire network, when possible. The optimization problem that results has been called the Target Set Selection Problem, and has been widely studied (see for eg. [8,3,40]): the goal is to find a minimum-sized set S ⊆ V that activates the entire network (if such a set exists). In a certain sense, the elements of this minimum target set S are the most influential people in the network; if they are activated, the entire network will eventually be activated.There are, however, two hidden flaws in the formulation of the target set problem. First, the nodes in the target set are as...

“…Chen [6] studied the Minimum Target Set problem under the LT model and proved a strong inapproximability result that makes unlikely the existence of an algorithm with approximation factor better than O(2 log 1− n ), where n is the number of nodes in the network. Chen's result stimulated a series of papers that isolated interesting cases in which the problem (and variants thereof) becomes tractable [1,2,3,5,10,11,12,14,15,16,18,19,20,26,36,37,43]. In the case of general networks, some efficient heuristics for the Minimum Target Set problem have been proposed in the literature [17,22,39].…”

Section: Introductionmentioning

confidence: 99%

On finding small sets that influence large networks

Rescigno

2016

Soc. Netw. Anal. Min.

Self Cite

We consider the problem of selecting a minimum size subset of nodes in a network, that allows to activate all the nodes of the network. We present a fast and simple algorithm that, in real-life networks, produces solutions that outperform the ones obtained by using the best algorithms in the literature. We also investigate the theoretical performances of our algorithm and give proofs of optimality for some classes of graphs. From an experimental perspective, experiments also show that the performance of the algorithms correlates with the modularity of the analyzed network. Moreover, the more the influence among communities is hard to propagate, the less the performances of the algorithms differ. On the other hand, when the network allows some propagation of influence between different communities, the gap between the solutions returned by the proposed algorithm and by the previous algorithms in the literature increases.