Limited Column Generation Technique for Several Telecommunication Network Design Problems

This paper presents a so-called Limited Column Generation technique for solving the Local Access Network Design and Expansion problems. We first define our models for the design problem and the expansion problem. Then, we formulate both problems into a tree-partitioning problem with exponential number of variables. Because its intersection graph is a chordal graph and, of course, a perfect graph, its linear programming relaxation has integral vertices. A dedicated column generation procedure is developed so that the master tree-partitioning linear program can be solved by just generating n columns, where n is the number of nodes in the network. Particularly, for the design problem, the subproblem of generating a column is the Tree Knapsack problem. We believe that such decomposition procedure provides not only an algorithm and a complexity bound for finding the exact optimal solution, but also a practical approach to solve real problems. Subject classification: Networks/graphs: applications, theory, tree algorithms. Programming: decomposition, column generation. Limited Column Generation Technique for Several Telecommunication Network Design Problems Dong Xiao Shaw