Approximating the single source unsplittable min-cost flow problem

Approximating the single source unsplittable min-cost flow problem

In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. Moreover, the total cost must not exceed a given budget. Thi...

On the Single-Source Unsplittable Flow Problem

If the necessary cut condition is satisfied, we show how to compute an unsplittable flow satisfying the demands such that the total flow through any edge exceeds its capacity by at most the maximum demand. For graphs in which all capacities are at least the maximum demand, we therefore obtain an unsplittable flow with congestion at most 2, and this result is best possible. Furthermore, we show ...

Single-Source Unsplittable Flow

The max-ow min-cut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity. Menger's theorem provides a good characterization for the following single{source disjoint paths problem: given a graph G, with a source vertex s and terminals t 1 ; : : :; t k , decide whether there exist edge{disjoint s-t i paths, for i = 1; : : :; k. W...

On the minimum cost multiple-source unsplittable flow problem

The minimum cost multiple-source unsplittable flow problem is studied in this paper. A simple necessary condition to get a solution is proposed. It deals with capacities and demands and can be seen as a generalization of the well-known semi-metric condition for continuous multicommdity flows. A cutting plane algorithm is derived using a superadditive approach. The inequalities considered here a...

Approximation Algorithms for Single-Source Unsplittable Flow