Multidimensional Spectral Load Balancing

We describe an algorithm for the static load balancing of scientific computations that generalizes and improves upon spectral bisection. Through a novel use of multiple eigenvectors, our new spectral algorithm can divide a computation into 4 or 8 pieces at once. These multidimensional spectral partitioning algorithms generate balanced partitions that have lower communication overhead and are less expensive to compute than those produced by spectral bisection. In addition, they automatically work to minimize message contention on a hypercube or mesh architecture. These spectral partitions are further improved by a multidimensional generalization of the KernighanLingraph partitioning algorithm. Results on several computational grids are given and compared with other popular methods. This work was supported by the Applied Mathematical Sciences program, U.S. Department of Energy, Office of Energy Research, and was performed at Sandia National Laboratories, operated for the U.S. Department of Energy under contract No. DE-AC04-76DP00789.