Least cost influence propagation in (social) networks

Fischetti, Matteo; Kahr, Michael; Leitner, Markus; Monaci, Michele; Ruthmair, Mario

doi:10.1007/s10107-018-1288-y

Cited by 28 publications

(63 citation statements)

References 24 publications

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“…When that is not the case, the formulation must add binary variables (one for each node) to keep track of the set of activated nodes at the end of the influence propagation process and embed the TU based integer programming formulation onto the subgraph defined by these activated nodes. In this regard, the recent paper by Fischetti et al [7] takes a big first step.…”

Section: Discussionmentioning

confidence: 99%

“…Subsequent to an earlier (working) version of our paper, Fischetti et al [7] considered the LCIP in a general setting where neighbors of a node may exert unequal influence, the entire network need not be influenced (i.e., 0 < ≤ 1), and the influence structure can be nonlinear. They proposed a novel set covering based formulation for this version of the LCIP.…”

Section: Related Literaturementioning

confidence: 99%

“…The objective (6) minimizes the total payments. Constraint set (7) requires the direction of influence over an arc should either be from i to j or from j to i. Constraint set (8) states that the summation of incentives given to node i and the incoming influence from active neighbors to i should be greater than or equal to the threshold for node i. Constraint set (9), called k-dicycle inequalities, enforces the condition that the directed influence propagation network formed by y, G(y), must be a DAG.…”

Section: Formulations For the Lcipmentioning

confidence: 99%

“…Before concluding this section, we discuss Fischetti et al's [7] experience with their approach when applied to the LCIP as defined in this paper. There are significant contrasts between our computational experiences.…”

Section: Testing the Proposed Branch-and-cut Approachmentioning

confidence: 99%

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A branch‐and‐cut approach for the least cost influence problem on social networks

2020

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This paper studies a problem in the online targeted marketing setting called the least cost influence problem (LCIP) that is known to be NP-hard. The goal is to find the minimum total amount of inducements (individuals to target and associated tailored incentives) required to influence a given population. We develop a branch-and-cut approach to solve this LCIP on arbitrary graphs. We build upon Günneç et al.'s novel totally unimodular (TU) formulation for the LCIP on trees. The key observation in applying this TU formulation to arbitrary graphs is to enforce an exponential set of inequalities that ensure the influence propagation network is acyclic. We also design several enhancements to the branch-and-cut procedure that improve its performance. We provide a large set of computational experiments on real-world graphs with up to 155 000 nodes and 327 000 edges that demonstrates the efficacy of the branch-and-cut approach. This branch-and-cut approach finds solutions that are on average 1.87% away from optimality based on a test-bed of 160 real-world graph instances. We also develop a heuristic that prioritizes nodes that receive low influence from their peers. This heuristic works particularly well on arbitrary graphs, providing solutions that are on average 1.99% away from optimality. Finally, we observe that partial incentives can result in significant cost savings, over 55% on average, compared to the setting where partial incentives are not allowed. KEYWORDSexact method, influence maximization, integer programming, strong formulation INTRODUCTIONOnline communication (through social networks, newspapers, blogs, shopping websites, etc.) has become one of the main resources for information sharing. A recent report (see [27]) shows that in the United States people consider online social networks to be one of the most effective ways for disseminating information, and two-thirds of the population use their online social networks as one of the channels for receiving information and news. Not surprisingly, people's decisions are affected by the information they receive through social media. While peer influence has been recognized as a role exerting an important impact in decision-making for a long time (see e.g., [1,2,9]), online social media provide a much easier and more convenient way to track the interaction of online customers based on their footprints. It opens an opportunity for researchers to understand social networks and manage their effects on purchasing decisions. The outcomes can be used as an essential part of creating successful online marketing strategies. As a result, there is an increasing interest in correctly identifying (targeting) customers that are most likely to help the spread of a product (or information) over a social network.Indeed, Chen [3] initiated a stream of work in this area focused on identifying the fewest number of nodes to target in order to influence an entire network. However, the mathematical models studied by Chen and many other researchers for such influence maximization pro...

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Section: Discussionmentioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

Section: Formulations For the Lcipmentioning

confidence: 99%

Section: Testing the Proposed Branch-and-cut Approachmentioning

confidence: 99%

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A branch‐and‐cut approach for the least cost influence problem on social networks

2020

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“…Recently, it has been observed that interest in researching and solving optimization problems related to the propagation of influence in social networks has increased 205,206 . Most of these problems are related to the identification of key players in the social network, which has critical importance for the process of influence propagation 207 . Although most of the current studies assume the well‐known propagation rates, scenarios in which the rates may increase dynamically for popular subjects are still a big challenge 208 …”

Section: Future Trendsmentioning

confidence: 99%

Semantic analysis on social networks: A survey

Bayrakdar

Yücedağ

Şimşek

et al. 2020

Int J Communication

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Summary As social networks are getting more and more popular day by day, large numbers of users becoming constantly active social network users. In this way, there is a huge amount of data produced by users in social networks. While social networking sites and dynamic applications of these sites are actively used by people, social network analysis is also receiving an increasing interest. Moreover, semantic understanding of text, image, and video shared in a social network has been a significant topic in the network analysis research. To the best of the author's knowledge, there has not been any comprehensive survey of social networks, including semantic analysis. In this survey, we have reviewed over 200 contributions in the field, most of which appeared in recent years. This paper not only aims to provide a comprehensive survey of the research and application of social network analysis based on semantic analysis but also summarizes the state‐of‐the‐art techniques for analyzing social media data. First of all, in this paper, social networks, basic concepts, and components related to social network analysis were examined. Second, semantic analysis methods for text, image, and video in social networks are explained, and various studies about these topics are examined in the literature. Then, the emerging approaches in social network analysis research, especially in semantic social network analysis, are discussed. Finally, the trending topics and applications for future directions of the research are emphasized; the information on what kind of studies may be realized in this area is given.

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Weighted target set selection on trees and cycles

Raghavan

Zhang

2020

Networks

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There is significant interest in understanding the dynamics of influence diffusion on a social network. The weighted target set selection (WTSS) problem is a fundamental viral marketing problem arising on social networks. In this problem, the goal is to select a set of influential nodes to target (e.g., for promoting a new product) that can influence the rest of the network. The WTSS problem is APX‐hard. With the goal of generating insights to solve the WTSS problem on arbitrary graphs, we study in this paper the WTSS problem on trees and cycles. For trees, we propose a linear‐time dynamic programming algorithm and present a tight and compact extended formulation. Furthermore, we project the extended formulation onto the space of the natural node variables yielding the polytope of the WTSS problem on trees. This projection leads to an exponentially sized set of valid inequalities whose polynomial‐time separation is also discussed. Next, we focus on cycles: we describe a linear‐time algorithm and present the complete description of the polytope for the WTSS problem on cycles. Finally, we describe how these formulations can be applied to arbitrary graphs.

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Least cost influence propagation in (social) networks

Cited by 28 publications

References 24 publications

A branch‐and‐cut approach for the least cost influence problem on social networks

A branch‐and‐cut approach for the least cost influence problem on social networks

Semantic analysis on social networks: A survey

Weighted target set selection on trees and cycles

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