NOTE ON POLYNOMIAL-TIME APPROXIMATION SCHEMES FOR INTEGRATED NETWORK DESIGN AND SCHEDULING PROBLEMS

In the integrated network design and scheduling (INDS) problem, we are asked to repair edges in a graph by using parallel machines so that the performance of the network is recovered by a certain level, and the objective is to minimize the makespan required to finish repairing edges. The main aim of this note is to show that polynomial-time approximation schemes exist for various families of the INDS problems with a constant number of parallel machines, including the problems associated with minimum spanning tree, shortest path, maximum edge-disjoint paths, and maximum-weight matching.