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BCIM: Budget and capacity constrained influence maximization in multilayer networks

Su-Su Zhang, Chuang Liu, Huijuan Wang, Yang Chen, Xiu-Xiu Zhan

TL;DR

The Budget and Capacity Constrained Influence Maximization problem within multilayer networks is proposed and a Multilayer Multi-population Genetic Algorithm (MMGA) is introduced to solve it, providing an effective and efficient solution to the problem.

Abstract

Influence maximization (IM) seeks to identify a seed set that maximizes influence within a network, with applications in areas such as viral marketing, disease control, and political campaigns. The budgeted influence maximization (BIM) problem extends IM by incorporating cost constraints for different nodes. However, the current BIM problem, limited by budget alone, often results in the selection of numerous low-cost nodes, which may not be applicable to real-world scenarios. Moreover, considering that users can transmit information across multiple social platforms, solving the BIM problem across these platforms could lead to more optimized resource utilization. To address these challenges, we propose the Budget and Capacity Constrained Influence Maximization (BCIM) problem within multilayer networks and introduce a Multilayer Multi-population Genetic Algorithm (MMGA) to solve it. The MMGA employs modules, such as initialization, repair, and parallel evolution, designed not only to meet budget and capacity constraints but also to significantly enhance algorithmic efficiency. Extensive experiments on both synthetic and empirical multilayer networks demonstrate that MMGA improves spreading performance by at least 10% under the two constraints compared to baselines extended from classical IM problems. The BCIM framework introduces a novel direction in influence maximization, providing an effective and efficient solution to the problem.

BCIM: Budget and capacity constrained influence maximization in multilayer networks

TL;DR

The Budget and Capacity Constrained Influence Maximization problem within multilayer networks is proposed and a Multilayer Multi-population Genetic Algorithm (MMGA) is introduced to solve it, providing an effective and efficient solution to the problem.

Abstract

Influence maximization (IM) seeks to identify a seed set that maximizes influence within a network, with applications in areas such as viral marketing, disease control, and political campaigns. The budgeted influence maximization (BIM) problem extends IM by incorporating cost constraints for different nodes. However, the current BIM problem, limited by budget alone, often results in the selection of numerous low-cost nodes, which may not be applicable to real-world scenarios. Moreover, considering that users can transmit information across multiple social platforms, solving the BIM problem across these platforms could lead to more optimized resource utilization. To address these challenges, we propose the Budget and Capacity Constrained Influence Maximization (BCIM) problem within multilayer networks and introduce a Multilayer Multi-population Genetic Algorithm (MMGA) to solve it. The MMGA employs modules, such as initialization, repair, and parallel evolution, designed not only to meet budget and capacity constraints but also to significantly enhance algorithmic efficiency. Extensive experiments on both synthetic and empirical multilayer networks demonstrate that MMGA improves spreading performance by at least 10% under the two constraints compared to baselines extended from classical IM problems. The BCIM framework introduces a novel direction in influence maximization, providing an effective and efficient solution to the problem.
Paper Structure (18 sections, 6 equations, 9 figures, 3 tables, 3 algorithms)

This paper contains 18 sections, 6 equations, 9 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary definition
  3. Problem Definition
  4. Multilayer independent cascade model
  5. Multilayer Multi-population Genetic Algorithm (MMGA)
  6. Initialization
  7. Repair Module
  8. Evolution
  9. Baselines and Datasets
  10. Baselines
  11. Empirical and synthetic multilayer networks
  12. Empirical multilayer networks
  13. Synthetic multilayer networks
  14. Experiment
  15. Parametric analysis
  16. ...and 3 more sections

Figures (9)

  • Figure 1: A schematic diagram of the MIC model in a three-layered network. We use red and blue to represent nodes in active and inactive states, respectively.
  • Figure 2: Framework of the multilayer multi-population genetic algorithm. (a) The initialization module generates $K$ populations. Each population contains $n$ individuals, which are selected from the multilayer network. (b) The crossover module exchanges certain nodes within individuals according to specific rules to generate new offspring. (c) The mutation module alters the nodes within the offspring generated in step (b) to randomly selected nodes. (d) The repair module aims to adjust the offspring that exceed the budget $B$. (e) The selection process retains the offspring with the higher fitness value as input for the next iteration.
  • Figure 3: Initialization of the multilayer multi-population genetic algorithm.
  • Figure 4: The repair module in the multi-population genetic algorithm.
  • Figure 6: Performance of MMGA with the change of crossover probability $p_c$ and evolutionary step. We set $p_m=0.005$, $K=20$, and $B=600$. The results are given for networks: (a) Transport; (b) CKM; (c) Drosophila; (d) ER; (e) WS; and (f) BA.
  • ...and 4 more figures