Multicommodity Flow Approximation Used for Exact Graph Partitioning

We present a fully polynomial-time approximation scheme for a multicommodity flow problem that yields lower bounds of the graph bisection problem. We compare the approximation algorithm with Lagrangian relaxation based cost-decomposition approaches and linear programming software when embedded in an exact branch&bound approach for graph bisection. It is shown that the approximation algorithm is clearly superior in this context. Furthermore, we present a new practical addition to the approximation algorithm which improves its performance distinctly. Finally, we prove the performance of the graph bisection algorithm using multicommodity flow approximation by computing formerly unknown bisection widths of some DeBruijnand Shuffle-Exchange-Graphs.