Optimizing cost flows by modifying arc costs and capacities

Abstract

We examine a network upgrade problem for cost flows. A budget can be distributed among the arcs of the network. An in- vestment on a single arc can be used either to decrease the arc flow cost, or to increase the arc capacity, or both. The goal is to maximize the flow through the network while not exceeding bounds on the budget and on the total flow cost. The problems are NP-hard even on series-parallel graphs. We provide an approximation algorithm on series-parallel graphs which, for arbitrary fi; " > 0, produces a solution which exceeds the bounds on the budget and the flow cost by factors 1+fi and 1+", respectively, while the amount of flow is at least that of an optimum solution. The running time of the algorithm is polynomial in the input size and 1=(fi").