Efficient algorithm to study interconnected networks

TL;DR

This paper introduces an efficient O(N log N) algorithm for analyzing the resilience of interconnected networks under failures, enabling the study of larger systems than previously possible.

Contribution

The authors develop a scalable algorithm that significantly improves the computational efficiency of percolation analysis in interconnected networks.

Findings

Algorithm scales as O(N log N), much faster than previous methods.

Applicable to any network topology and failure sequence.

Enables analysis of larger interconnected networks.

Abstract

Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address these questions is the percolation model, where the resilience of the system is quantified by the dependence of the size of the largest cluster on the number of failures. Numerically, the major challenge is the identification of this cluster and the calculation of its size. Here, we propose an efficient algorithm to tackle this problem. We show that the algorithm scales as O(N log N), where N is the number of nodes in the network, a significant improvement compared to O(N^2) for a greedy algorithm, what permits studying much larger networks. Our new strategy can be applied to any network topology and distribution of interdependencies, as well as any sequence of failures.