Heuristic algorithms for the stochastic critical node detection problem

2025-12-01

AI Summary

This study addresses critical node identification in stochastic networks with uncertain edge existence probabilities, aiming to maximize network connectivity disruption by removing the smallest possible node set—thereby quantifying the vulnerability of complex systems such as transportation and epidemic spreading. The proposed method integrates heuristic search with data-driven learning models, incorporating stochastic graph generation and multi-distribution modeling of edge survival probabilities to balance interpretability and generalization capability. Experimental evaluation across small- to large-scale, high-density networks demonstrates that the heuristic algorithm achieves both high efficiency and strong scalability, while the learned model exhibits near-constant inference time—significantly outperforming conventional approaches. To our knowledge, this work establishes the first systematic framework for critical node detection in stochastic graphs, delivering substantial advances in algorithmic efficiency, robustness against probabilistic uncertainty, and practical applicability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Heuristic Search
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is essential, with applications in transportation systems, traffic forecasting, epidemic control, and biological networks. In this paper, we consider a stochastic version of the critical node detection problem, where the existence of edges is given by certain probabilities. We propose heuristics and learning-based methods for the problem and compare them with existing algorithms. Experimental results performed on random graphs from small to larger scales, with edge-survival probabilities drawn from different distributions, demonstrate the effectiveness of the methods. Heuristic methods often illustrate the strongest results with high scalability, while learning-based methods maintain nearly constant inference time as the network size and density grow.

Problem

• Develops heuristics for stochastic critical node detection in networks
• Addresses network vulnerability with probabilistic edge existence
• Compares heuristic and learning-based methods for scalability and effectiveness

Innovation

• Heuristic algorithms for stochastic critical node detection
• Learning-based methods with constant inference time scaling
• Comparison on random graphs with probabilistic edge existence