🤖 AI Summary
This paper addresses the graph dismantling problem under edge-budget constraints for spatially embedded planar graphs (e.g., transportation and power grids), aiming to quantify the impact of edge removal on network connectivity robustness. We propose a “spanning-tree skeleton–dual-path” framework: multiple spanning trees are uniformly sampled to construct a structural skeleton; combined with logarithmic density feature estimation and a slope-prediction model, the framework adaptively selects either fine-grained dismantling (for small budgets) or rapid fragmentation (for large budgets). The method ensures both interpretability and computational efficiency, achieving near-linear time complexity on random planar graphs. It significantly reduces the size of the largest connected component and uncovers a clear quantitative relationship between edge budget and fragmentation extent. This work establishes a novel paradigm for robustness assessment of critical infrastructure networks.
📝 Abstract
In spatially embedded networks such as transportation and power grids, understanding how edge removals affect connectivity is crucial for robustness analysis. This paper studies a planar graph dismantling problem under an edge-budget constraint. We propose a spanning-tree-skeleton dual-path framework that first samples multiple uniform spanning trees to capture network backbones and then adaptively selects between two complementary paths according to the budget. The small-budget path estimates a dismantlable subgraph fraction using a logarithmic density feature, while the large-budget path predicts the optimal partition count through a slope-based model. Experiments on random planar graphs demonstrate near-linear runtime scaling, consistent reductions in the largest connected component ratio, and clear budget-fragmentation trends. The method provides an interpretable and efficient approach for planar-network robustness analysis.