A linear programming approach to increasing the weight of all minimum spanning trees

Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. Frederickson and Solis-Oba gave an algorithm for the case when the costs are linear, we give a different derivation of their algorithm and we slightly extend it to deal with convex piecewise linear costs. For that we formulate the problem as a combinatorial linear program and show how to produce primal and dual solutions.

• Type: Journal
• Year: 2008
• Where: NETWORKS
• Authors: Mourad Baïou, Francisco Barahona
• Keywords: Computer Networks, Linear, Minimum Cost Increase, Minimum Spanning Trees, NETWORKS 2008