A constrained capacity expansion problem on networks

In this paper we consider a type of constrained maximum capacity path (CMCP) problem which can be described as how to increase the capacity vector of a network so that the capacities of the maximum capacity path for every pair of nodes in the network can be increased to the maximum extent while the total cost for the increment of capacity is within a given budget limit. We transform this problem into solving some minimum spanning tree problems and propose a strongly polynomial algorithm for this problem. Finally we discuss other methods and show the advantage of the proposed algorithm.