Influence Maximization Problem Research Articles

IMNE: Maximizing influence through deep learning-based node embedding in social network

Influence Maximization (IM) is a critical problem in social network analysis and marketing. It involves identifying a subset of nodes in a social network whose activation or influence can lead to the maximal spread of information, ideas, or behaviors within the network. Although many approaches have been developed in the literature to deal with this problem, most of these approaches are ineffective in dealing with large-scale social networks due to free parameters and computational complexity. Embeddings are used to learn low-dimensional representations of nodes in a social network. These embeddings capture the structural and semantic information of nodes and their relationships within the network. By training deep learning models on graph-structured data, node embeddings can capture complex patterns and dependencies in social networks, enabling more effective downstream tasks such as IM. Accordingly, this paper proposes an efficient algorithm to address the IM problem in social networks using deep learning-based Node Embedding (IMNE), which includes shell decomposition, graph/node embedding, and search space reduction as well as the use of local structural features. Our approach combines the power of deep learning for representation learning with the rich structural information present in social networks to address the challenge of IM in complex and dynamic social networks. IMNE uses the Independent Cascade (IC) information diffusion model to determine the labels needed to train the model by calculating the influence of nodes. Experimental results on several real-world networks considering different performance metrics show that IMNE performs better compared to existing baseline and state-of-the-art methods.

DCDIMB: Dynamic Community-based Diversified Influence Maximization using Bridge Nodes

Influence maximization (IM) is the fundamental study of social network analysis. The IM problem finds the top k nodes that have maximum influence in the network. Most of the studies in IM focus on maximizing the number of activated nodes in the static social network. But in real life, social networks are dynamic in nature. This work addresses the diversification of activated nodes in the dynamic social network. This work proposes an objective function that maximizes the number of communities by utilizing bridge nodes. We also propose a diffusion model that considers the role of inactive nodes in influencing a node. We prove the submodularity, and monotonicity of the objective function under the proposed diffusion model. This work analyzes the impact of different ratios of bridge nodes in the seed set on real-world and synthetic datasets. Further, we prove the NP-Hardness of the objective function under the proposed diffusion model. The experiments are conducted on various real-world and synthetic datasets with known and unknown community information. The proposed work experimentally shows that the objective function gives the maximum number of communities considering bridge nodes compared to the benchmark algorithms.

A cost-effective seed selection model for multi-constraint influence maximization in social networks

The Influence Maximization (IM) problem aims to maximize the diffusion of information or adoption of products among users within a social network by identifying and activating a set of initial users. It is not unrealistic to have a higher activation cost for more influential users in real-life applications. However, existing works on IM focus solely on finding the most influential users as the seed set, without considering either the activation costs of individual nodes and the total budget or the size of the seed set. This oversight may lead to infeasible solutions, particularly from financial and managerial perspectives, respectively. To address these issues, we propose a more realistic and generalized formulation called Multi-Constraint Influence Maximization (MCIM) to achieve a cost-effective solution under both budgetary and cardinality constraints. The MCIM model allows for variable-length solutions, necessitating the exclusion of seed nodes from the influence spread estimation. Consequently, unlike existing IM formulations, the spread function under the MCIM model is no longer monotonic but submodular. As it has also been proven to be an NP-hard problem, we propose a Simple Additive Weighting (SAW)-assisted Differential Evolution (DE) algorithm for solving large-size real-world IM problems. Experimental results on four datasets demonstrate the effectiveness of the proposed formulation and algorithm in finding optimal and cost-effective solutions.

Being an influencer is hard: The complexity of influence maximization in temporal graphs with a fixed source

We consider the influence maximization problem over a temporal graph, where there is a single fixed source. We deviate from the standard model of influence maximization, where the goal is to choose the set of most influential vertices. Instead, in our model we are given a fixed vertex, or source, and the goal is to find the best time steps to transmit so that the influence of this vertex is maximized. We frame this problem as a spreading process that follows a variant of the susceptible-infected-susceptible (SIS) model and we focus on four objective functions. In the MaxSpread objective, the goal is to maximize the total number of vertices that get infected at least once. In the MaxViral objective, the goal is to maximize the number of vertices that are infected at the same time step. In the MaxViralTstep objective, the goal is to maximize the number of vertices that are infected at a given time step. Finally, in MinNonViralTime, the goal is to maximize the total number of vertices that are infected in every d time step window. We perform a thorough complexity theoretic analysis for these four objectives over three different scenarios: (1) the unconstrained setting where the source can transmit whenever it wants; (2) the window-constrained setting where the source has to transmit at either a predetermined, or a shifting window; (3) the periodic setting where the temporal graph has a small period.

GraMeR: Graph Meta Reinforcement Learning for Multi-Objective Influence Maximization

Influence maximization (IM) is a combinatorial problem of identifying a subset of seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, its practical uses are limited due to the computational complexity of current algorithms. Recently, deep reinforcement learning has been leveraged to solve IM in order to ease the computational burden. However, there are serious limitations in current approaches, including narrow IM formulation that only consider influence via spread and ignore self activation, low scalability to large graphs, and lack of generalizability across graph families leading to a large running time for every test network. In this work, we address these limitations through a unique approach that involves: (1) Formulating a generic IM problem as a Markov decision process that handles both intrinsic and influence activations; (2) incorporating generalizability via meta-learning across graph families. There are previous works that combine deep reinforcement learning with graph neural network but this work solves a more realistic IM problem and incorporates generalizability across graphs via meta reinforcement learning. Extensive experiments are carried out in various standard networks to validate performance of the proposed Graph Meta Reinforcement learning (GraMeR) framework. The results indicate that GraMeR is multiple orders faster and generic than conventional approaches when applied on small to medium scale graphs.

Finding robust and influential nodes from networks under cascading failures using a memetic algorithm

In the research of complex networks, how to find a set of nodes in the network with the most extensive range in the propagation process, i.e., the Influence Maximization (IM) problem, is one of the focal topics. Existing studies mainly consider the information dissemination process on networks and how to select diffusive nodes efficiently, but little attention has been paid to changes related to the network structure. In reality, networked systems are exposed to uncertain interferences and even destructive sabotages, and cascading failures are one common destruction that can cause networks to collapse even if only a small number of nodes fail. In the case of various complex environmental factors, how to select robust and influential nodes, i.e., the robust influence maximization (RIM) problem, is of great importance in promoting the realistic application of the influence maximization problem. This paper investigates the RIM problem under cascading failures to address the shortcomings in previous studies. Based on existing research, a new performance evaluation metric, RS-cf, is designed to assess the level of robust influence in a numerical form. For solving the seed determination problem, a Memetic algorithm towards the RIM problem under cascading failures, MA-RIMCF, is designed to find nodes with stable information propagation capability guided by RS-cf. Experiments have been conducted on both synthetic and realistic networks to validate the performance of the algorithm. Results indicate that MA-RIMCF can obtain competitive candidates over existing approaches, and seeds with robust and influential abilities are generated to solve diffusion dilemmas.

Fuzzy Influence Maximization in Social Networks

Influence maximization is a fundamental problem in social network analysis. This problem refers to the identification of a set of influential users as initial spreaders to maximize the spread of a message in a network. When such a message is spread, some users may be influenced by it. A common assumption of existing work is that the impact of a message is essentially binary: A user is either influenced (activated) or not influenced (non-activated). However, how strongly a user is influenced by a message may play an important role in this user’s attempt to influence subsequent users and spread the message further; existing methods may fail to model accurately the spreading process and identify influential users. In this article, we propose a novel approach to model a social network as a fuzzy graph where a fuzzy variable is used to represent the extent to which a user is influenced by a message (user’s activation level). By extending a diffusion model to simulate the spreading process in such a fuzzy graph, we conceptually formulate the fuzzy influence maximization problem for which three methods are proposed to identify influential users. Experimental results demonstrate the accuracy of the proposed methods in determining influential users in social networks.

Finding robust and influential nodes on directed networks using a memetic algorithm

The influence maximization problem is a research hotspot on social networks, which involves selecting a set of nodes as seeds to maximize the influence spread. The robust influence maximization problem is a further extension of the influence maximization problem considering the external factors pertaining to the propagation process. The current research mainly includes how to select the most influential nodes through algorithms, or how to improve the robustness of the network structure. However, these researches lack the application of the propagation models in directed networks, and also ignore the networked robustness on the information transmission. Therefore, this paper focuses on analyzing the characteristics of directed networks in the information propagation process, and further solve the robust influence maximization problem considering the directionality. First, a robust influence evaluation factor RSD is designed to assess the robust influence ability of each node on directed networks. Under the guidance of this evaluation factor, a problem-directed Memetic algorithm is developed to solve the robust influence maximization problem, named MA-RIMD. The characteristics of directed networks are considered involving with the genetic operators. The empirical analysis on several synthetic and practical networks indicates that MA-RIMD can select robust and influential seeds from directed networks, outperforming baseline approaches. Based on experiments conducted on three synthetic networks and two real-world networks, our proposed algorithm exhibits a performance improvement up to 15% over baseline approaches.

Performance Evaluation of EvolutionaryAlgorithms on Solving the InfluenceMaximization Problem in Social Networks

Performance Evaluation of EvolutionaryAlgorithms on Solving the InfluenceMaximization Problem in Social Networks

ToupleGDD: A Fine-Designed Solution of Influence Maximization by Deep Reinforcement Learning

Aiming at selecting a small subset of nodes with maximum influence on networks, the Influence Maximization (IM) problem has been extensively studied. Since it is #P-hard to compute the influence spread given a seed set, the state-of-the-art methods, including heuristic and approximation algorithms, faced with great difficulties such as theoretical guarantee, time efficiency, generalization, etc. This makes it unable to adapt to large-scale networks and more complex applications. On the other side, with the latest achievements of Deep Reinforcement Learning (DRL) in artificial intelligence and other fields, lots of works have been focused on exploiting DRL to solve combinatorial optimization problems. Inspired by this, we propose a novel end-to-end DRL framework, ToupleGDD, to address the IM problem in this paper, which incorporates three coupled graph neural networks for network embedding and double deep Q-networks for parameters learning. Previous efforts to solve IM problem with DRL trained their models on subgraphs of the whole network, and then tested on the whole graph, which makes the performance of their models unstable among different networks. However, our model is trained on several small randomly generated graphs with a small budget, and tested on completely different networks under various large budgets, which can obtain results very close to IMM and better results than OPIM-C on several datasets, and shows strong generalization ability. Finally, we conduct a large number of experiments on synthetic and realistic datasets, and experimental results prove the effectiveness and superiority of our model.

Fairness-Aware Competitive Bidding Influence Maximization in Social Networks

Competitive influence maximization (CIM) has been studied for years due to its wide application in many domains. Most current studies primarily focus on the microlevel optimization by designing policies for one competitor to defeat its opponents. Furthermore, current studies ignore the fact that many influential nodes have their own starting prices, which may lead to inefficient budget allocation. In this article, we propose a novel competitive bidding influence maximization (CBIM) problem, where the competitors allocate budgets to bid for the seeds attributed to the platform during multiple bidding rounds. To solve the CBIM problem, we propose a fairness-aware multiagent CBIM (FMCBIM) framework. In this framework, we present a multiagent bidding particle environment (MBE) to model the competitors’ interactions and design a starting price adjustment mechanism to model the dynamic bidding environment. Moreover, we put forward a novel multiagent CBIM (MCBIM) algorithm to optimize competitors’ bidding policies. Extensive experiments on five datasets show that our work has good efficiency and effectiveness.

The Impact of Passive Social Media Viewers in Influence Maximization

A frequently studied problem in the context of digital marketing for online social networks is the influence maximization problem that seeks for an initial seed set of influencers to trigger an information propagation cascade (in terms of active message forwarders) of expected maximum impact. Previously studied problems typically neglect that the probability that individuals passively view content without forwarding it is much higher than the probability that they forward content. Considering passive viewing enables us to maximize more natural (social media) marketing metrics, including (a) the expected organic reach, (b) the expected number of total impressions, or (c) the expected patronage, all of which are investigated in this paper for the first time in the context of influence maximization. We propose mathematical models to maximize these objectives, whereby the model for variant (c) includes individual’s resistances and uses a multinomial logit model to model customer behavior. We also show that these models can be easily adapted to a competitive setting in which the seed set of a competitor is known. In a computational study based on network graphs from Twitter (now X) and from the literature, we show that one can increase the expected patronage, organic reach, and number of total impressions by 36% on average (and up to 13 times in particular cases) compared with seed sets obtained from the classical maximization of message-forwarding users. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the Federal Ministry of Education, Science and Research of Austria and by the Austrian Agency for International Mobility and Cooperation in Education, Science and Research [Reference ICM-2019-13384]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0047 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0047 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Graph Bayesian Optimization for Multiplex Influence Maximization

Influence maximization (IM) is the problem of identifying a limited number of initial influential users within a social network to maximize the number of influenced users. However, previous research has mostly focused on individual information propagation, neglecting the simultaneous and interactive dissemination of multiple information items. In reality, when users encounter a piece of information, such as a smartphone product, they often associate it with related products in their minds, such as earphones or computers from the same brand. Additionally, information platforms frequently recommend related content to users, amplifying this cascading effect and leading to multiplex influence diffusion. This paper first formulates the Multiplex Influence Maximization (Multi-IM) problem using multiplex diffusion models with an information association mechanism. In this problem, the seed set is a combination of influential users and information. To effectively manage the combinatorial complexity, we propose Graph Bayesian Optimization for Multi-IM (GBIM). The multiplex diffusion process is thoroughly investigated using a highly effective global kernelized attention message-passing module. This module, in conjunction with Bayesian linear regression (BLR), produces a scalable surrogate model. A data acquisition module incorporating the exploration-exploitation trade-off is developed to optimize the seed set further. Extensive experiments on synthetic and real-world datasets have proven our proposed framework effective. The code is available at https://github.com/zirui-yuan/GBIM.

Heterogeneous network influence maximization algorithm based on multi-scale propagation strength and repulsive force of propagation field

Heterogeneous networks, like social and academic networks are widespread in the real world, characterized by diverse nodes and complex relationships. Influence maximization is a crucial research topic, in these networks, as it can help in comprehending the mechanisms of information propagation and diffusion. Effectively utilizing complex structural information poses a challenge in current research on influence maximization in heterogeneous information networks. As a solution to this problem, a heterogeneous network influence maximization algorithm based on the multi-scale propagation strength and repulsive force of propagation field is proposed. Firstly, based on the propagation field, we design a multi-scale propagation strength index for the propagation ability of nodes to achieve maximum coverage of influence propagation. Specifically, in the homogeneous structure, the homogeneous propagation strength describes the propagation ability of nodes. In the heterogeneous structure, the heterogeneous shallow propagation strength and the heterogeneous deep propagation strength are designed to exploit the local and global spreading ability of nodes using meta-paths and link prediction based on graph neural networks, respectively. Secondly, to ensure the minimum overlap in the propagation range of seed nodes, we designed the overlapping repulsive force between node pairs in the propagation field. Finally, considering the complexity of the propagation process of heterogeneous information networks, an independent cascade model based on meta-paths is proposed. Based on experiments conducted with several datasets, our algorithm outperforms baseline algorithms for solving influence maximization problem.

Adaptive Influence Maximization: Adaptability via Nonadaptability

Adaptive influence maximization is an important research problem in computational social networks, which is also a typical problem in the study of adaptive processing of information and adaptive construction of objects. In this paper, we propose a new method that reduces the adaptive influence maximization problem into a nonadaptive one in a different social network, so that an adaptive optimization can be solved by those methods for nonadaptive optimization. In addition, we provide a new approximation algorithm for the submodular maximization problem with a knapsack constraint, which runs in [Formula: see text] time and has performance ratio [Formula: see text], where n is the number of nodes in the network. The ratio is better than the best known previous one with the same running time. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This research is supported in part by the National Natural Science Foundation of China [Grant U20A2068].

A genetic algorithm concerning diversity information for solving the robust influence maximization problem on networks

The influence maximization problem is one of the hot research topics in the field of complex networks in recent years. The so-called influence maximization problem is how to select the seed set that propagates the largest amount of information on a given network. In practical applications, networks are often exposed to complicated environments, and both link-specific and node-specific attacks can have a significant impact on the network’s propagation performance. Several pilot studies have revealed the crux of the robust influence maximization problem, but the current work available is not comprehensive. On the one hand, existing studies only consider the case that the network structure is stable or under link-specific attacks, and few researches have concentrated on the case when the network structure is under node-specific attacks. On the other hand, the current algorithm fails to combine the information of the search process well to solve the robust influence maximization problem. Aiming at these deficiencies, in this paper, a metric for evaluating the robust influence performance of seeds under node-specific attacks is developed. Guided by this, a genetic algorithm (GA) maintaining the principle of diversity concern (DC) to solve the Robust Influence Maximization (RIM) problem is designed, called DC-GA-RIM. DC-GA-RIM contains several problem-orientated operators and fully considers diverse information in the optimization process, which significantly improves the search ability of the algorithm. The effectiveness of DC-GA-RIM in solving the RIM problem is demonstrated on a variety of networks. The superiority of this algorithm over other approaches is shown.

A New Algorithm Framework for the Influence Maximization Problem Using Graph Clustering

Given a social network modelled by a graph, the goal of the influence maximization problem is to find k vertices that maximize the number of active vertices through a process of diffusion. For this diffusion, the linear threshold model is considered. A new algorithm, called ClusterGreedy, is proposed to solve the influence maximization problem. The ClusterGreedy algorithm creates a partition of the original set of nodes into small subsets (the clusters), applies the SimpleGreedy algorithm to the subgraphs induced by each subset of nodes, and obtains the seed set from a combination of the seed set of each cluster by solving an integer linear program. This algorithm is further improved by exploring the submodularity property of the diffusion function. Experimental results show that the ClusterGreedy algorithm provides, on average, higher influence spread and lower running times than the SimpleGreedy algorithm on Watts–Strogatz random graphs.

Influence maximization based on threshold models in hypergraphs.

Influence maximization problem has received significant attention in recent years due to its application in various domains, such as product recommendation, public opinion dissemination, and disease propagation. This paper proposes a theoretical analysis framework for collective influence in hypergraphs, focusing on identifying a set of seeds that maximize influence in threshold models. First, we extend the message passing method from pairwise networks to hypergraphs to accurately describe the activation process in threshold models. Then, we introduce the concept of hypergraph collective influence (HCI) to measure the influence of nodes. Subsequently, we design an algorithm, HCI-TM, to select the influence maximization set, taking into account both node and hyperedge activation. Numerical simulations demonstrate that HCI-TM outperforms several competing algorithms in synthetic and real-world hypergraphs. Furthermore, we find that HCI can be used as a tool to predict the occurrence of cascading phenomena. Notably, we find that the HCI-TM algorithm works better for larger average hyperdegrees in Erdös-Rényi hypergraphs and smaller power-law exponents in scale-free hypergraphs.

A Graph Sampling-Based Model for Influence Maximization in Large-Scale Social Networks

Social networks have attracted a great deal of attention and have, in fact, changed the way we produce, consume, and diffuse information. This change gave rise to the notion of social influence and today we talk about influential nodes. The process of detecting influential nodes in social networks aims to find entities that propagate information to a large portion of the network users. This process is often known as the influence maximization (IM) problem. Due to the explosive growth of social networks’ data, their structure is more complex and we talk about “big graph data.” Moreover, modern networks are dynamic and their topology or/and information is likely to change over time. Detecting influential nodes in such networks is a challenging task. Several methods have been developed in this context. However, they concentrate on static networks and there is little work on large-scale social networks. We propose in this article a new model for IM called MapReduce-based dynamic selection of influential nodes (MR-DSINs) that has the ability to cope with the huge size of real social networks. In fact, our approach is based on a graph sampling step in order to reduce the network’s size. Given that reduced version, MR-DSIN is able to select dynamically influential nodes. Our proposal has the advantage of considering the dynamics of information that can be modeled by users’ social actions (e.g.“, share”, “comment”, “retweet”). Experimental results on real-world social networks and computer-generated artificial graphs demonstrate that MR-DSIN is efficient for identifying influential nodes, compared with three known proposals. We prove that our model is able to detect in the reduced graph an influence as important as in the original one.

Supplementary Influence Maximization Problem in Social Networks

Due to important applications in viral marketing, influence maximization (IM) has become a well-studied problem. It aims at finding a small subset of initial users so that they can deliver information to the largest amount of users through the word-of-mouth effect. The original IM only considers a singleton item. And the majority of extensions ignore the relationships among different items or only consider their competitive interactions. In reality, the diffusion probability of one item will increase when users adopted supplementary products in advance. Motivated by this scenario, we propose a supplementary independent cascade (IC) and discuss the supplementary IM problem. Our problem is NP-hard, and the computation of the objective function is #P-hard. We notice that the diffusion probability will change when considering the impact of its supplementary product. Therefore, the efficient reverse influence sampling (RIS) techniques cannot be applied to our problem directly even though the objective function is submodular. To address this issue, we utilize the sandwich approximation (SA) strategy to obtain a data-dependent approximate solution. Furthermore, we define the supplementary-based reverse reachable (SRR) sets and then propose a heuristic algorithm. Finally, the experimental results on three real datasets support the efficiency and superiority of our methods.