Abstract:

This paper considers a capacity expansion problem with budget constraint. Suppose each edge in the network has two attributes: capacity and the degree of difficulty.The difficulty degree of a tree T is the maximum degree of difficulty of all edges in the tree and the cost for coping with the difficulty in a tree is a nondecreasing function about the difficulty degree of the tree. The authors need to increase capacities of some edges so that there is a spanning tree whose capacity can be increased to the maximum extent, meanwhile the total cost for increasing capacity as well as overcoming the difficulty in the spanning tree does not exceed a given budget D. Suppose the cost for increasing capacity on each edge is a linear function about the increment of capacity, they transform this problem into solving some hybrid parametric spanning tree problems[1] and propose a strongly polynomial algorithm.

Key words: Capacity expansion, minimum spanning tree, bottleneck spanning tree, poly-nomial complexity.