  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.
