k-way Hypergraph Partitioning via n-Level Recursive Bisection

Abstract

We develop a multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time. Using several caching and lazy-evaluation techniques during coarsening and refinement, we reduce the running time by up to two-orders of magnitude compared to a naive n-level algorithm that would be adequate for ordinary graph partitioning. The overall performance is even better than the widely used hMetis hypergraph partitioner that uses a classical multilevel algorithm with few levels. Aided by a portfolio-based approach to initial partitioning and adaptive budgeting of imbalance within recursive bipartitioning, we achieve very high quality. We assembled a large benchmark set with 310 hypergraphs stemming from application areas such VLSI, SAT solving, social networks, and scientific computing. We achieve significantly smaller cuts than hMetis and PaToH, while being faster than hMetis. Considerably larger improvements are observed for some instance classes like social networks, for bipartitioning, and for partitions with an allowed imbalance of 10%. The algorithm presented in this work forms the basis of our hypergraph partitioning framework KaHyPar (Karlsruhe Hypergraph Partitioning).

Engineering a direct k-way Hypergraph Partitioning Algorithm

“…n-level algorithms have been used in geometric data structures based on randomized incremental construction [36,37] and as a preprocessing technique for route planning [38]. Furthermore, the n-level paradigm has been successfully employed in both graph and hypergraph partitioning: KaSPar [28] is a direct k-way graph partitioner, KaHyPar [19] is based on recursive bipartitioning and currently seems to be the method of choice for optimizing the cut-metric unless speed is more important than quality. There is an unpublished attempt to design a direct k-way n-level hypergraph partitioner that optimizes the cut-net metric [39].…”

“…Despite several interesting ideas and good quality in the majority of experiments, this algorithm has not been able to improve on the state of the art consistently in terms of the time-quality trade-off. The highly tuned n-level direct k-way partitioner presented here optimizes the (λ − 1)-metric, but builds on the ideas and insights gathered during the development of both hypergraph partitioning algorithms [19,39]. To the best of our knowledge, a multilevel version of Sanchis' k-way FM algorithm [24] has only been implemented in [17] to optimize the total message latency of parallel matrix vector multiplies by partitioning hypergraphs with very few (≤ 128) nets.…”

“…In [19] our group developed a hypergraph partitioner based on recursive bisection that achieves high quality partitions for the cut-net metric using a very fine grained "n-level" approach, removing only one vertex in every layer of the hierarchy. In this paper, we adopt the n-level approach but otherwise use significantly more sophisticated techniques.…”

“…In Section 5.1 we then present a simple and fast coarsening algorithm that eliminates the bottlenecks of [19] without affecting the overall solution quality. The initial partitioning algorithm is described briefly in Section 5.2.…”

“…Previous work [15,[25][26][27] explicitly mentions these problems as reasons for sticking to simple greedy algorithms. We overcome these problems by generalizing the gain caching and updating strategies from [19] to the (considerably more complex) k-way case. We also develop an adaptive stopping rule that generalizes a previous solution for n-level graph partitioning [28].…”