A new iterative refinement scheme is proposed for both 1D and 2D partitioning. A binary search algorithm is proposed for 2D jagged partitioning by introducing a new 2D probing scheme. Binary search method is successfully adopted to 1D striped decomposition by deriving and exploiting a good upper bound on the value of an optimal solution. Both asymptotically and run time efficient exact algorithms are proposed and implemented for one dimensional (1D) striping and two dimensional (2D) jagged partitioning. Optimal load balancing in sparse matrix decomposition without disturbing the row/column ordering is investigated. The end result is that our hybrid CPU+GPU environment, hereafter referred to simply as GPU environment, delivers an energy-delay product that is multiple orders of magnitude better than a traditional CPU environment, whether unicore or multicore.
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Specifically, we take an important biological code that runs in a traditional CPU environment and transform and map it to a hybrid CPU+GPU environment. This paper seeks to characterize, and perhaps debunk, the notion of a ldquopower-hungry GPUrdquo via an empirical study of the performance, power, and energy characteristics of GPUs for scientific computing. As a consequence, the GPU has been viewed as a ldquonon-greenrdquo computing solution. For example, the NVIDIA GTX 280 video card is rated at 236 watts, which is as much as the rest of a compute node, thus requiring a 500-W power supply.
However, while today's state-of-the-art GPU can easily reduce the execution time of a parallel code by many orders of magnitude, it arguably comes at the expense of significant power and energy consumption. The graphics processing unit (GPU) has emerged as a computational accelerator that dramatically reduces the time to discovery in high-end computing (HEC).
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