Network Flow-Based Refinement for Multilevel Hypergraph Partitioning

We present a refinement framework for multilevel hypergraph partitioning that uses max-flow computations on pairs of blocks to improve the solution quality of a k -way partition. The framework generalizes the flow-based improvement algorithm of the Karlsruhe Fast Flow Partitioner (KaFFPa) from graphs to hypergraphs and is integrated into the hypergraph partitioner Karlsruhe Hypergraph Partitioning (KaHyPar). By reducing the size of hypergraph flow networks, improving the flow model used in KaFFPa, and developing techniques to improve the running time of our algorithm, we obtain a partitioner that computes the best solutions for a wide range of benchmark hypergraphs from different application areas for both the connectivity and the cut-net metric while still having a running time comparable to that of hMetis. In the case of graph partitioning, our algorithm compares favorably with KaFFPa, even after enhancing the latter with our improved flow network, and at the same time is more than a factor of two faster. Finally, we show that our algorithm improves the performance of the memetic multilevel hypergraph partitioner KaHyPar-E.