A class of network capacity expansion problem with N constraints

The paper considers a class of bottleneck capacity expansion problem on networks. network N (V, E, C) is given and the capacity vector C is increased so that the capacity of the maximum-capacity tree can be increased to the maximum extent while the total cost (both fixed cost and increasing cost) for the increment of capacity is within a given budget limit, the total time (span time between the start time and finish time) for the increment of capacity is within a given time limit and other more given constraints are within their own limits. After studying the feature of this network capacity expansion problem, the paper proposes a strong polynomial algorithm to solve the problem.