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

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.