An Incremental Algorithm for Checking the Possibility of Braess Paradox in Dynamic Nets

Braess paradox is a well-known phenomenon that originates when latency at Wardrop equilibrium in traffic networks decreases because of removing edges. The possibility of having the paradox was called vulnerability by Roughgarden in 2006 and was characterized later on by graph-theoretical notions, both for undirected and for directed graphs. In this paper we provide an algorithm for the incremental case of checking vulnerability for dynamically evolving graphs. The crucial idea to keep the amortized cost linear for every edge addition is that we do not need to run the vulnerability algorithm on the whole graph, but only on a well-identified subgraph, determined by the edge that we are adding. Overall, to add m edges, we pay a cost of O(m2); this aligns with the O(m2) cost of the state-of-the-art static algorithm for vulnerability.