Graph Bisection with Pareto-Optimization

Abstract: We introduce FlowCutter, a novel algorithm to compute a set of edge cuts or node separators that optimize cut size and balance in the Pareto-sense. Our core algorithm solves the balanced connected st-edge-cut problem, where two given nodes s and t must be separated by removing edges to obtain two connected parts. Using the core algorithm we build variants that compute node separators and are independent of s and t. Using the Pareto-set we can identify cuts with a particularly good trade-off between cut size and balance that can be used to compute contraction and minimum fill-in orders, which can be used in Customizable Contraction Hierarchies (CCH), a speed-up technique for shortest path computations. Our core algorithm runs in O(cm) time where m is the number of edges and c the cut size. This makes it well-suited for large graphs with small cuts, such as road graphs, which are our primary application. For road graphs we present an extensive experimental study demonstrating that FlowCutter outperforms the current state of the art both in terms of cut sizes as well as CCH performance.