Least-Cost Influence Maximization on Social Networks

Günneç, Dilek; Raghavan, S.; Zhang, Rui

doi:10.1287/ijoc.2019.0886

Cited by 22 publications

(43 citation statements)

References 20 publications

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“…In this paper, we design and test a branch-and-cut approach for solving the LCIP on arbitrary graphs. We build upon the TU formulation for trees described in Günneç et al [12]. In Section 2, we present formulations for the LCIP on arbitrary graphs.…”

Section: Our Contributionsmentioning

confidence: 99%

“…As we will see in Section 4, this formulation is weak and even the LP relaxation cannot be solved for large networks. Günneç et al [12] described a formulation based on influence propagation over arcs specific to trees. We enhance that model to apply it to arbitrary graphs.…”

Section: Formulations For the Lcipmentioning

confidence: 99%

“…Furthermore, its linear relaxation does not provide integral solutions on trees (note that on trees constraint set (9) is deleted) which we know to solve polynomially. We describe a third formulation for the LCIP, HLZ, that builds on the TU formulation for trees introduced by Günneç et al [12]. This model further characterizes the incoming influence at a given node i.…”

Section: Arc∶ Minmentioning

confidence: 99%

“…Notice that when the underlying graph is a tree, constraint set (16) becomes redundant because constraint set (17) rules out all cycles with two arcs and there are no cycles with three or more arcs when the underlying graph is a tree. Thus, if we substitute constraint set (15) into constraint set (17), we obtain the TU formulation in Günneç et al [12].…”

Section: Arc∶ Minmentioning

confidence: 99%

“…It selects the node with the smallest influence factor among the inactive nodes in each iteration and pays it the threshold value. While it seems counterintuitive to select the node whose neighbors exert the smallest influence (on it), Günneç et al [12] showed that the influence greedy heuristic solves the LCIP on trees optimally (indicating this strategy can indeed be effective). Over all our test instances, the influence greedy almost always gives a strictly better solution (236 out of 240 instances).…”

Section: Initial Feasible Solutionmentioning

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: Our Contributionsmentioning

confidence: 99%

Section: Formulations For the Lcipmentioning

confidence: 99%

Section: Arc∶ Minmentioning

confidence: 99%

Section: Arc∶ Minmentioning

confidence: 99%

Section: Initial Feasible Solutionmentioning

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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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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Efficient presolving methods for the influence maximization problem

Chen

Dai

et al. 2023

Networks

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We consider the influence maximization problem (IMP) which asks for identifying a limited number of key individuals to spread influence in a network such that the expected number of influenced individuals is maximized. The stochastic maximal covering location problem (SMCLP) formulation is a mixed integer programming formulation that effectively approximates the IMP by the Monte‐Carlo sampling. For IMPs with a large‐scale network or a large number of samplings, however, the SMCLP formulation cannot be efficiently solved by existing exact algorithms due to its large problem size. In this paper, we attempt to develop presolving methods to reduce the problem size and hence enhance the capability of employing exact algorithms in solving large‐scale IMPs. In particular, we propose two effective presolving methods, called strongly connected nodes aggregation (SCNA) and isomorphic nodes aggregation (INA), respectively. The SCNA enables to build a new SMCLP formulation that is potentially much more compact than the existing one, and the INA further eliminates variables and constraints in the SMCLP formulation. A theoretical analysis on two special cases of the IMP is provided to demonstrate the strength of the SCNA and INA in reducing the problem size of the SMCLP formulation. We integrate the proposed presolving methods, SCNA and INA, into the Benders decomposition algorithm, which is recognized as one of the state‐of‐the‐art exact algorithms for solving the IMP. We show that the proposed SCNA and INA provide the possibility to develop a much faster separation algorithm for the Benders cuts. Numerical results demonstrate that with the SCNA and INA, the Benders decomposition algorithm is much more effective in solving the IMP in terms of solution time.

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Least-Cost Influence Maximization on Social Networks

Cited by 22 publications

References 20 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

Weighted target set selection on trees and cycles

Efficient presolving methods for the influence maximization problem

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