Heuristic algorithms for the stochastic critical node detection problem
Tuguldur Bayarsaikhan, Altannar Chinchuluun, Ashwin Arulselvan, Panos Pardalos
TL;DR
This work tackles stochastic critical node detection (SCNDP) by addressing edge-uncertainty through both heuristics and graph neural networks. It introduces REGA and several greedy-based strategies, along with an edge-aware GraphSAGE-GAT framework trained on REGA-derived labels, plus curriculum learning for scalability. Across synthetic networks, the approaches achieve competitive disruption of connectivity with favorable runtimes, and learning-based methods offer near-constant inference times as size grows. The results highlight the value of combining reduced stochastic formulations, efficient EPC estimation, and learning-based inference for large-scale, uncertain networks.
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.