A Decremental Algorithm for Checking the Possibility of Braess Paradox in Dynamic Nets

2026-10-05

AI Summary

This study addresses the prohibitive computational cost of detecting Braess paradox vulnerability in dynamic networks. Grounded in Wardrop equilibrium theory, it proposes a decremental algorithm achieving linear amortized time complexity per edge deletion. Methodologically, the approach optimizes the dynamic graph detection process by marking irrelevant edges and refines existing static algorithms, reducing their complexity from O(nm²) to O(m²) to enable efficient dynamic updates. The core contribution lies in ensuring that each edge deletion operation incurs only linear amortized time complexity. This advancement significantly enhances the efficiency of vulnerability analysis in large-scale dynamic networks, demonstrating clear superiority over existing methods.

Abstract

Braess paradox originates when latency at Wardrop equilibrium in traffic networks decreases because of removing edges. The graph-theoretic property of networks suffering from the Braess paradox was called vulnerability by Roughgarden in 2006; it was then characterized and algorithmically checked both for undirected and for directed nets. In this paper, we provide a decremental algorithm of linear amortized complexity to check vulnerability for dynamically evolving networks. The basic idea of our dynamic algorithm is to use a static algorithm that marks some edges as irrelevant for the vulnerability of the graph and ignore those edges for all subsequent runs of the decremental procedure. To get a linear amortized cost for every edge remotion, we also provide a new version of such a static algorithm that improves its complexity from O(n m^2) to O(m^2), that is in turn aligned with the cost of the best state-of-the-art static algorithm for vulnerability.

Problem

• Braess paradox
• dynamic networks
• vulnerability
• decremental algorithm
• traffic networks

Innovation

• Braess paradox
• decremental algorithm
• dynamic networks
• vulnerability
• amortized complexity