Improved max-flow min-cut algorithms in a Circular Disk Failure Model with application to a road network

In the evaluation of network reliability, the objectives are to model reliability of networks appropriately and to compute it in a realistic time. We can consider various models of reliability of networks, and Bienstock (1991) first introduced a geographical failure model where each failure is represented by a 2‐dimensional region. In this model, we consider the situation that geographical networks such as road networks may be damaged by externally caused disasters, and such disasters may destroy several links of the networks simultaneously, rather than each link independently. Recently, Neumayer–Efrat–Modiano (2012) investigated the max‐flow problem and the min‐cut problem under the Circular Disk Failure Model, in which the shape of each failure is restricted to be a disk. Under this model, Kobayashi–Otsuki (2014) gave polynomial time algorithms to find optimal solutions of these two problems. In this paper, we improve the algorithms and evaluate their performance by computational experiments. Although our improvements work only when the max‐flow value is equal to the min‐cut value, this condition holds in almost all practical cases. Owing to the improvements, we can find in a realistic time optimal solutions of the max‐flow problem and the min‐cut problem in large networks under the Circular Disk Failure Model. As a realistic instance, we analyze reliability of a road network in NewYork consisting of 264,346 nodes.