Before revision:  This differs from traditional graph or hypergraph partitioning models which minimize total communication under a work balance constraint. We address regimes where partitions of the row space and column space are expected to match (the symmetric case) or are allowed to differ (the nonsymmetric case) .
After revision:  This differs from traditional graph or hypergraph partitioning models which minimize total communication , or from traditional load balancing models which only balance work. One can view our algorithms as optimally rounding one-dimensional embeddings of direct K-way noncontiguous partitioning problems .