Before revision:  We propose exact and approximate contiguous partitioners that minimize the maximum runtime of any processor under a diverse family of cost models that combine work and hypergraph communication terms in symmetric or asymmetric settings. This differs from traditional 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. Our algorithms use linear space.
After revision:  We propose the first near-linear time algorithms for several graph partitioning problems in the contiguous regime. Traditional objectives such as the simple edge cut, hyperedge cut, or hypergraph connectivity minimize the total cost of all parts under a balance constraint. Our total partitioners use O(Km + N) space. They run in O((Km\log(m) + N)\log(N)) time, a significant improvement over prior O(K(m^2 + N)) time algorithms due to Kernighan and Grandjean et. al. Bottleneck partitioning minimizes the maximum cost of any part. We propose a new bottleneck cost which reflects the sum of communication and computation on each part. Our bottleneck partitioners use linear space.