Task mapping on supercomputers with cellular networks

This thesis focuses on techniques of task mapping for solving problems on parallel computers with hundreds of thousands of processors on cellular networks. Task mapping is a serious intellectual challenge and a practical tool for unleashing the potential power of supercomputers. It is challenging because of both the astronomical searching space and the high dependence on the exact nature of the applications and the computers. In this thesis, we propose two general static mapping models to optimize the assignment of tasks on heterogeneous, distributed-memory, ultra-scalable computers. In our models, the underlying application problems can be appropriately decomposed to subtasks with known computational load and known inter-task communicational demands. We also know, or can conveniently measure, the computing systems' specifications such as individual processor speed and inter-processor communication cost. Our models abstract an application as a demand matrix and a parallel computer as a load matrix and a supply matrix with which we construct our models as minimizing the objective function value for completing the application on the given computer. We have tested several applications on Blue Gene/L supercomputer with 3D mesh and torus networks. For a 2D wave equation, the mappings generated by our models reduced communication by 51% for 3D-mesh and 31% for 3D-torus over the default MPI rank order mapping. For SMG2000 application, our mapping can reduce communication and total time by 16% and 5% over the default MPI rank order mapping, respectively. For NPB MG, we improve the communication time and benchmark result by 53% and 13%, respectively. For NPB CG, we improve the communication time and benchmark result by 43% and 22%, respectively. We believe that our models are useful for task assignment for broad applications on a family of supercomputers with cellular networks.