  The balanced hypergraph partitioning problem is to partition a hypergraph
into $k$ disjoint blocks of bounded size such that the sum of the number of
blocks connected by each hyperedge is minimized. We present an improvement to
the flow-based refinement framework of KaHyPar-MF, the current state-of-the-art
multilevel $k$-way hypergraph partitioning algorithm for high-quality
solutions. Our improvement is based on the recently proposed HyperFlowCutter
algorithm for computing bipartitions of unweighted hypergraphs by solving a
sequence of incremental maximum flow problems. Since vertices and hyperedges
are aggregated during the coarsening phase, refinement algorithms employed in
the multilevel setting must be able to handle both weighted hyperedges and
weighted vertices -- even if the initial input hypergraph is unweighted. We
therefore enhance HyperFlowCutter to handle weighted instances and propose a
technique for computing maximum flows directly on weighted hypergraphs.
  We compare the performance of two configurations of our new algorithm with
KaHyPar-MF and seven other partitioning algorithms on a comprehensive benchmark
set with instances from application areas such as VLSI design, scientific
computing, and SAT solving. Our first configuration, KaHyPar-HFC, computes
slightly better solutions than KaHyPar-MF using significantly less running
time. The second configuration, KaHyPar-HFC*, computes solutions of
significantly better quality and is still slightly faster than KaHyPar-MF.
Furthermore, in terms of solution quality, both configurations also outperform
all other competing partitioners.
