Applicability of the Minimal Dominating Set for Influence Maximisation in Multilayer Networks

2025-02-21

AI Summary

This paper addresses the seed selection problem for cross-community collaborative influence maximization in multilayer networks (MLNs). We propose a Minimum Dominating Set (MDS)-based optimization framework, integrating the Linear Threshold Model (LTM) with inter-layer AND/OR influence aggregation mechanisms. Our method comprises a localized MDS refinement algorithm and a rank-optimized seed filtering strategy. To our knowledge, this work is the first to systematically establish the conditional validity of MDS for influence propagation in MLNs. Experimental results demonstrate that MDS significantly enhances influence coverage under large seed budgets, low activation thresholds, and AND-type aggregation—attributable to its cross-layer structural domination property rather than universal optimality. The key contribution lies in identifying MDS as particularly effective for scenarios requiring holistic, cross-layer cooperative penetration, while rigorously characterizing its theoretical validity boundaries. This provides both foundational insights and practical tools for modeling multilayer social influence.

Technology Category

• Multiagent Systems: Other Foundations of Multi Agent Systems
• Application Domains: Humanities & Computational Social Science
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Content-based information diffusion
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The minimal dominating set (MDS) is a well-established concept in network controllability and has been successfully applied in various domains, including sensor placement, network resilience, and epidemic containment. In this study, we adapt the local-improvement MDS routine and explore its potential for enhancing seed selection for influence maximisation in multilayer networks (MLN). We employ the Linear Threshold Model (LTM), which offers an intuitive representation of influence spread or opinion dynamics by accounting for peer influence accumulation. To ensure interpretability, we utilise rank-refining seed selection methods, with the results further filtered with MDS. Our findings reveal that incorporating MDS into the seed selection process improves spread only within a specific range of situations. Notably, the improvement is observed for larger seed set budgets, lower activation thresholds, and when an"AND"strategy is used to aggregate influence across network layers. This scenario reflects situations where an individual does not require the majority of their acquaintances to hold a target opinion, but must be influenced across all social circles.

Problem

• Minimal Dominating Set applicability
• Influence Maximisation in Multilayer Networks
• Linear Threshold Model seed selection

Innovation

• Minimal Dominating Set adaptation
• Linear Threshold Model utilization
• Rank-refining seed selection methods