Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy [article]

Zhicheng Guo, Jiaxuan Zhao, Licheng Jiao, Xu Liu
2021 arXiv   pre-print
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
more » ... rn 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.
arXiv:2106.07501v1 fatcat:vwxsskx2kzdaxmchkk7c3kmkxm