High-Quality Hypergraph Partitioning

Abstract

Hypergraphs are a generalization of graphs where edges (aka nets ) are allowed to connect more than two vertices. They have a similarly wide range of applications as graphs. This article considers the fundamental and intensively studied problem of balanced hypergraph partitioning (BHP) , which asks for partitioning the vertices into k disjoint blocks of bounded size while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric . We describe our open-source hypergraph partitioner KaHyPar which is based on the successful multi-level approach—driving it to the extreme of using one level for (almost) every vertex. Using carefully designed data structures and dynamic update techniques, this approach turns out to have a very good time–quality tradeoff. We present two preprocessing techniques— pin sparsification using locality-sensitive hashing (LSH) and community detection based on the Louvain algorithm . The community structure is used to guide the coarsening process that incrementally contracts vertices. Portfolio-based partitioning of the contracted hypergraph then already achieves a good initial solution. While reversing the contraction process, a combination of several refinement techniques achieves a good final partitioning. In particular, we support a highly-localized local search that can directly produce a k -way partitioning and complement this with flow-based techniques that take a more global view. Optionally, a memetic algorithm evolves a pool of solution candidates to an overall good solution. We evaluate KaHyPar for a large set of instances from a wide range of application domains. With respect to quality, KaHyPar outperforms all previously considered systems that can handle large hypergraphs such as hMETIS, PaToH, Mondriaan, or Zoltan. Somewhat surprisingly, to some extend, this even extends to graph partitioners such as KaHIP when considering the special case of graphs. KaHyPar is also faster than most of these systems except for PaToH which represents a different speed–quality tradeoff.