A Spanning-Tree-Based Algorithm for Planar Graph Dismantling

TL;DR

This paper introduces a novel spanning-tree-based algorithm for dismantling planar graphs under edge constraints, enabling efficient robustness analysis of spatial networks like transportation and power grids.

Contribution

It presents a dual-path framework that adaptively estimates network dismantling metrics using spanning trees, improving efficiency and interpretability over existing methods.

Findings

Near-linear runtime scaling demonstrated on random planar graphs.

Significant reduction in the largest connected component with increased budget.

Clear trends in network fragmentation as budget varies.

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.