Maximum Capacity Path Problem with Arc Reversal

In a network with capacitated arcs, the maximum capacity path problem is to find the bottleneck path between two nodes that has the maximum capacity among all the paths between the nodes. In this work, a problem of identification of such a path is considered allowing arc reversals in a directed graph where the capacity of the reversed arc can be added to the capacity of its counterpart. We propose an O(m) algorithm to solve the problem in a directed graph with  arcs.