Hybrid connectivity-oriented efficient shielding for robustness enhancement in large-scale networks

Abstract

Network infrastructure protection is critical for ensuring robustness against attacks and failures, yet existing approaches fundamentally limit their scope by addressing either node or edge vulnerabilities in isolation — an unrealistic assumption given real-world scenarios where both element types may fail simultaneously. Our work makes three key advances beyond current state-of-the-art: First, we introduce the novel concept of hybrid connectivity as a unified robustness metric that properly accounts for concurrent node-edge failures, demonstrating through theoretical analysis that traditional single-element metrics require prohibitively high connectivity thresholds. Second, we develop the first practical solution for large-scale networks via our hybrid cut-tree mapping algorithm, which employs an extended node cut formulation with dynamic programming to identify all vulnerable node-edge combinations in linear time — a dramatic complexity reduction from the exponential scaling of existing linear programming methods. Third, we prove and exploit a fundamental structural property that shielding any edge spanning tree plus leaf edges guarantees target hybrid connectivity, enabling our edge spanning tree algorithm to deliver near-optimal solutions at unprecedented scale. Experimental validation confirms our approach maintains 100% protection effectiveness (with no more than 6% cost overhead versus optimal) in small graphs while achieving 99.9% protection coverage in large-scale networks — outperforming all existing heuristics in protection cost while providing a $10^5$ times speedup over traditional methods.