通过Wasserstein差异实现多级超图划分的平衡粗化
Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy
AI总结：
针对多级超图划分，本文提出结合LPT先验、Wasserstein差异与Sinkhorn最优传输的平衡粗化方案，并利用Fiedler向量归一化割及三点算法改进初始k路划分。
摘要：
我们提出了一种用于多级超图划分的平衡粗化方案。此外，设计了一种初始划分算法以提升k路超图划分的质量。通过LPT算法分配顶点权重，我们在松弛的平衡约束下生成先验超图。借助该先验超图，我们定义了Wasserstein差异，以协调粗化过程的最优传输；并通过Sinkhorn算法求解最优传输矩阵。我们的粗化方案充分考虑了连通性度量（目标函数）的最小化。在初始划分阶段，我们定义了由Fiedler向量诱导的归一化割函数，并在理论上证明其为凹函数。据此，设计了一种三点算法，用于在平衡约束下寻找最佳割。
英文摘要：
We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT algorithm, we generate a prior hypergraph under a relaxed balance constraint. With the prior hypergraph, we have defined the Wasserstein discrepancy to coordinate the optimal transport of coarsening process. And the optimal transport matrix is solved by Sinkhorn algorithm. Our coarsening scheme fully takes into account the minimization of connectivity metric (objective function). For the initial partitioning stage, we define a normalized cut function induced by Fiedler vector, which is theoretically proved to be a concave function. Thereby, a three-point algorithm is designed to find the best cut under the balance constraint.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
