The influence maximization problem has gained particular importance in viral marketing for large-scale spreading in social networks. Developing a fast and appropriate algorithm to identify an optimized seed set for the diffusion process on social networks is crucial due to the fast growth of networks. Most fast methods only focus on the degree of nodes while ignoring the strategic position of nodes in the networks. These methods do not have the required quality in finding a seed set in most networks. On the other hand, many other methods have acceptable quality, but their computational overhead is significant. To address these issues, the main concentration of this paper is to propose a fast and accurate method for the influence maximization problem, which uses a local traveling for labeling of nodes based on the influence power, called the LMP algorithm. In the proposed LMP algorithm, first, a travel starts from a node with the lowest influence power to assign a ranking-label for this node and its neighbor nodes in each step based on their diffusion capability and strategic position. The LMP algorithm uses node labeling steps to reduce search space significantly. Three ranking-labels are used in the proposed algorithm, and nodes with the highest ranking-label are selected as candidate nodes. This local and fast step strictly reduces the search space. Finally, the LMP algorithm selects seed nodes based on the topology features and the strategic position of the candidate and connector. The performance of the proposed algorithm is benchmarked with the well-known and recently proposed seed selection algorithms. The experimental results are performed on real-world and synthetic networks to validate the efficiency and effectiveness. The experiments exhibit that the proposed algorithm is the fastest in comparison with other state-of-the-art algorithms, and it has linear time complexity. In addition, it can achieve a good tradeoff between the efficiency and time complexity in the influence maximization problem. 

Influence maximization problem by leveraging the local traveling and node labeling method for discovering most influential nodes in social networks

The problem of maximizing a normalized monotone non-submodular set function subject to a cardinality constraint arises in the context of extracting information from massive streaming data. In this paper, we present four streaming algorithms for this problem by utilizing the concept of diminishing-return ratio. We analyze these algorithms to obtain the corresponding approximation ratios, which generalize the previous results for the submodular case. The numerical experiments show that our algorithms have better solution quality and competitive running time when compared to an existing algorithm.

Non-submodular maximization on massive data streams

Given a fixed total budget and a predefined cost model, the budgeted influence maximization problem aims to find a subset of nodes to maximize the influence spread in social networks while its cost should be no more than the fixed total budget. In this paper, we propose a local-global influence indicator based constrained evolutionary algorithm, named IICEA, to solve the budgeted influence maximization problem effectively and efficiently. In IICEA, a novel influence indicator is firstly designed by considering two components: local neighbor information and global community information, which can be used to better measure the influence of nodes in social networks. Based on the proposed local-global influence indicator, we propose a constrained evolutionary framework by designing several novel strategies such as mutation strategy, crossover strategy and repairment strategy to promote the evolution of population. Experimental results on 10 real-world social networks demonstrate the effectiveness of the proposed local-global influence indicator and also verify the effectiveness and efficiency of the proposed algorithm IICEA in comparison with several variant versions of IICEA and several representative baseline algorithms.

A Local-Global Influence Indicator Based Constrained Evolutionary Algorithm for Budgeted Influence Maximization in Social Networks

Submodular optimization plays a significant role in combinatorial problems, since it captures the structure of the edge cuts in graphs, the coverage of sets, and so on. Many data mining and machine learning problems can be cast as submodular maximization problems with applications in recommendation systems and data diversification. In this paper, we focus on the problem of maximizing a monotone submodular function subject to a $d$ -knapsack constraint, for which we propose a streaming algorithm that achieves a $(({1}/{1+2d})-\epsilon)$ -approximation of the optimal value, while it only needs one single pass through the data set without storing all the data in the memory. In our experiments, we extensively evaluate the effectiveness of our proposed algorithm via two applications: news recommendation and scientific literature recommendation. It is observed that the proposed streaming algorithm achieves both execution speedup and memory saving by several orders of magnitude, compared with existing approaches.

Streaming Algorithms for News and Scientific Literature Recommendation: Monotone Submodular Maximization With a $d$ -Knapsack Constraint

With the proliferation of social networks, the Influence Maximization (IM), which identifies the influential users for target marketing, gains enormous research interest in recent years. However, most of the existing IM studies ignore the seeding cost estimation, which is the minimum number of nodes that are required to activate the seed nodes. Moreover, the existing Reverse Influence Maximization (RIM) models are incapable of resolving the challenging issues appropriately. Therefore, in this paper, we propose an efficient Knapsack-based RIM solution (KRIM) under the Linear Threshold model, which returns the optimized seeding cost. The experimental results show that our model outperforms the existing RIM models.

https://dl.acm.org/doi/pdf/10.1145/3297280.3297621

Knapsack-based reverse influence maximization for target marketing in social networks

In a social network, influence maximization is the problem of identifying a set of users that own the maximum influence ability across the network. In this paper, a novel credit distribution (CD)-based model, termed as the multiaction CD (mCD) model, is introduced to quantify the influence ability of each user, which works with practical datasets where one type of action could be recorded for multiple times. Based on this model, influence maximization is formulated as a submodular maximization problem under a general knapsack constraint, which is NP hard. An efficient streaming algorithm with one-round scan over the user set is developed to find a suboptimal solution. Specifically, we first solve a special case of knapsack constraints, i.e., a cardinality constraint, and show that the developed streaming algorithm can achieve ( $({1}/{2})-\epsilon $ ) approximation of the optimality. Furthermore, for the general knapsack case, we show that the modified streaming algorithm can achieve ( $({1}/{3})-\epsilon $ ) approximation of the optimality. Finally, experiments are conducted over real Twitter dataset and demonstrate that the mCD model enjoys high accuracy compared to the conventional CD model in estimating the total number of people who get influenced in a social network. Moreover, through the comparison to the conventional CD, non-CD models, and the mCD model with the greedy algorithm on the performance of the influence maximization problem, we show the effectiveness and efficiency of the proposed mCD model with the streaming algorithm.

Fast Budgeted Influence Maximization Over Multi-Action Event Logs

In a social network, influence maximization is the problem of identifying a set of users that own the maximum {\it influence ability} across the network. In this paper, a novel credit distribution (CD) based model, termed as the multi-action CD (mCD) model, is introduced to quantify the influence ability of each user, which works with practical datasets where one type of action could be recorded for multiple times. Based on this model, influence maximization is formulated as a submodular maximization problem under a general knapsack constraint, which is NP-hard. An efficient streaming algorithm with one-round scan over the user set is developed to find a suboptimal solution. Specifically, we first solve a special case of knapsack constraints, i.e., a cardinality constraint, and show that the developed streaming algorithm can achieve ($\frac{1}{2}-\epsilon$)-approximation of the optimality. Furthermore, for the general knapsack case, we show that the modified streaming algorithm can achieve ($\frac{1}{3}-\epsilon$)-approximation of the optimality. Finally, experiments are conducted over real Twitter dataset and demonstrate that the mCD model enjoys high accuracy compared to the conventional CD model in estimating the total number of people who get influenced in a social network. Moreover, through the comparison to the conventional CD, non-CD models, and the mCD model with the greedy algorithm on the performance of the influence maximization problem, we show the effectiveness and efficiency of the proposed mCD model with the streaming algorithm.

Fast Budgeted Influence Maximization over Multi-Action Event Logs

In a social network, influence maximization is the problem of identifying a set of users that own the maximum influence ability across the network. In this paper, a novel credit distribution (CD) based model, termed as the multi-action CD (mCD) model, is introduced to quantify the influence ability of each user. Compared to existing models, the new model can work with practical datasets where one type of action is recorded for multiple times. Based on this model, influence maximization is formulated as a submodular maximization problem under a knapsack constraint, which is NP-hard. An efficient streaming algorithm is developed to achieve $(\frac{1}{3}-\epsilon)$ approximation of the optimality. Experiments conducted on real Twitter dataset demonstrate that the mCD model enjoys high accuracy compared to the conventional CD model in estimating the total number of people who get influenced in a social network. Furthermore, compared to the greedy algorithm, the proposed single-pass streaming algorithm achieves similar performance in terms of influence maximization, while running several orders of magnitude faster.

Streaming Influence Maximization in Social Networks Based on Multi-Action Credit Distribution

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Fast Budgeted Influence Maximization Over Multi-Action Event Logs

Fast Budgeted Influence Maximization over Multi-Action Event Logs

Streaming Influence Maximization in Social Networks Based on Multi-Action Credit Distribution