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.

Processing large complex networks like social networks or web graphs has attracted considerable interest. To do this in parallel, we need to partition them into pieces of roughly equal size. Unfortunately, previous parallel graph partitioners originally developed for more regular mesh-like networks do not work well for complex networks. Here we address this problem by parallelizing and adapting the label propagation technique originally developed for graph clustering. By introducing size constraints, label propagation becomes applicable for both the coarsening and the refinement phase of multilevel graph partitioning. This way we exploit the hierarchical cluster structure present in many complex networks. We obtain very high quality by applying a highly parallel evolutionary algorithm to the coarsest graph. The resulting system is both more scalable and achieves higher quality than state-of-theart systems like ParMetis or PT-Scotch. For large complex networks the performance differences are very big. As an example, our algorithm partitions a web graph with 3.3 G edges in 16 seconds using 512 cores of a high-performance cluster while producing a high quality partition-none of the competing systems can handle this graph on our system.

In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the past decade in practical algorithms for balanced (hyper)graph partitioning together with future research directions. Our work serves as an update to a previous survey on the topic [ 29 ]. In particular, the survey extends the previous survey by also covering hypergraph partitioning and has an additional focus on parallel algorithms.