Sensitivity analysis on the all pairs q-route flows in a network

Given an undirected edge‐weighted network in which one edge capacity is allowed to vary, we propose in this paper a polynomial algorithm that needs only two 2‐cut‐trees computations to provide the all pairs maximum 2‐route flow values. Moreover, we provide an extension to the case where k edge capacities may vary, and show that 2k 2‐cut‐trees computations are necessary in order to determine the all pairs maximum 2‐route‐flow values. This makes our algorithm polynomial whenever .