Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across k different blocks of bounded size, such that hyperedges span as few parts as possible. This problem is well-studied in sequential and distributed settings, but not in shared-memory. We close this gap by devising efficient and scalable shared-memory algorithms for all components employed in the best sequential solvers without compromises with regards to solution quality.

This work presents the scalable and high-quality hypergraph partitioning framework Mt-KaHyPar. Its most important components are parallel improvement algorithms based on the FM algorithm and maximum flows, as well as a parallel clustering algorithm for coarsening – which are used in a multilevel scheme with log (n) levels. As additional components, we parallelize the n-level partitioning scheme, devise a deterministic version of our algorithm, and present optimizations for plain graphs.

We evaluate our solver on more than 800 graphs and hypergraphs, and compare it with 25 different algorithms from the literature. Our fastest configuration outperforms almost all existing hypergraph partitioners with regards to both solution quality and running time. Our highest-quality configuration achieves the same solution quality as the best sequential partitioner KaHyPar, while being an order of magnitude faster with ten threads. Thus, two of our configurations occupy all fronts of the Pareto curve for hypergraph partitioning. Furthermore, our solvers exhibit good speedups, e.g., 29.6x in the geometric mean on 64 cores (deterministic), 22.3x (log (n)-level), and 25.9x (n-level).

平衡超图划分对于许多应用来说都是一个 NP 难题，例如优化分布式数据放置问题中的通信。目标是将所有节点放置在 k 个不同的有界大小的块上，以便超边跨越尽可能少的部分。这个问题在顺序和分布式设置中得到了充分研究，但在共享内存中却没有。我们通过为最佳顺序求解器中使用的所有组件设计高效且可扩展的共享内存算法来缩小这一差距，而不会影响解决方案的质量。

这项工作提出了可扩展且高质量的超图划分框架 Mt-KaHyPar。其最重要的组成部分是基于 FM 算法和最大流的并行改进算法，以及用于粗化的并行聚类算法 - 这些算法用于具有 log ( n ) 级别的多级方案。作为附加组件，我们并行化n级分区方案，设计算法的确定性版本，并提出对普通图的优化。

我们在 800 多个图和超图上评估我们的求解器，并将其与文献中的 25 种不同算法进行比较。在解决方案质量和运行时间方面，我们最快的配置优于几乎所有现有的超图分区器。我们的最高质量配置实现了与最佳顺序分区器 KaHyPar 相同的解决方案质量，同时在十个线程下速度提高了一个数量级。因此，我们的两个配置占据了超图划分帕累托曲线的所有前沿。此外，我们的求解器表现出良好的加速比，例如，64 核上的几何平均值为 29.6 倍（确定性）、22.3 倍（log ( n ) 级）和 25.9 倍（n级）。