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The current trend of performance growth in HPC systems is accompanied by a massive increase in energy consumption. In this article, we introduce GreenMD, an energy-efficient framework for heterogeneous systems for LU factorization utilizing multi-GPUs. LU factorization is a crucial kernel from the MAGMA library, which is highly optimized. Our aim is to apply DVFS to this application by leveraging slacks intelligently on both CPUs and multiple GPUs. To predict the slack times, accurate performance models are developed separately for both CPUs and GPUs based on the algorithmic knowledge and manufacturer’s specifications. Since DVFS does not reduce static energy consumption, we also develop undervolting techniques for both CPUs and GPUs. Reducing voltage below threshold values may give rise to errors; hence, we extract the minimum safe voltages ( V safeMin ) for the CPUs and GPUs utilizing a low overhead profiling phase and apply them before execution. It is shown that GreenMD improves the CPU, GPU, and total energy about 59%, 21%, and 31%, respectively, while delivering similar performance to the state-of-the-art linear algebra MAGMA library. 

The k-core of a graph is the largest induced sub-graph with minimum degree k. The problem of k-core decomposition finds the k-cores of a graph for all valid values of k, and it has many applications such as network analysis, computational biology and graph visualization. Currently, there are two types of parallel algorithms for k-core decomposition: (1) degree-based vertex peeling, and (2) iterative h-index refinement. There is, however, few studies on accelerating k-core decomposition using GPU. In this paper, we propose a highly optimized peeling algorithm on a GPU, and compare it with possible implementations on top of think-like-a-vertex graph-parallel GPU systems as well as existing serial and parallel k-core decomposition algorithms on CPUs. Extensive experiments show that our GPU algorithm is the overall winner in both time and space. Our source code is released at https://github.com/akhlaqueak/KCoreGPU. 

The increase of computer processing speed is significantly outpacing improvements in network and storage bandwidth, leading to the big data challenge in modern science, where scientific applications can quickly generate much more data than that can be transferred and stored. As a result, big scientific data must be reduced by a few orders of magnitude while the accuracy of the reduced data needs to be guaranteed for further scientific explorations. Moreover, scientists are often interested in some specific spatial/temporal regions in their data, where higher accuracy is required. The locations of the regions requiring high accuracy can sometimes be prescribed based on application knowledge, while other times they must be estimated based on general spatial/temporal variation. In this paper, we develop a novel multilevel approach which allows users to impose region-wise compression error bounds. Our method utilizes the byproduct of a multilevel compressor to detect regions where details are rich and we provide the theoretical underpinning for region-wise error control. With spatially varying precision preservation, our approach can achieve significantly higher compression ratios than single-error bounded compression approaches and control errors in the regions of interest. We conduct the evaluations on two climate use cases – one targeting small-scale, node features and the other focusing on long, areal features. For both use cases, the locations of the features were unknown ahead of the compression. By selecting approximately 16% of the data based on multi-scale spatial variations and compressing those regions with smaller error tolerances than the rest, our approach improves the accuracy of post-analysis by approximately 2 × compared to single-error-bounded compression at the same compression ratio. Using the same error bound for the region of interest, our approach can achieve an increase of more than 50% in overall compression ratio. 

Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is arguably the most efficient Entropy coding algorithm in information theory, such that it could be found as a fundamental step in many modern compression algorithms such as DEFLATE. On the other hand, today's HPC applications are more and more relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, resulting in a significant bottleneck in the entire data processing. In this paper, we propose and implement an efficient Huffman encoding approach based on modern GPU architectures, which addresses two key challenges: (1) how to parallelize the entire Huffman encoding algorithm, including codebook construction, and (2) how to fully utilize the high memory-bandwidth feature of modern GPU architectures. The detailed contribution is four-fold. (1) We develop an efficient parallel codebook construction on GPUs that scales effectively with the number of input symbols. (2) We propose a novel reduction based encoding scheme that can efficiently merge the codewords on GPUs. (3) We optimize the overall GPU performance by leveraging the state-of-the-art CUDA APIs such as Cooperative Groups. (4) We evaluate our Huffman encoder thoroughly using six real-world application datasets on two advanced GPUs and compare with our implemented multi-threaded Huffman encoder. Experiments show that our solution can improve the encoding throughput by up to 5.0x and 6.8x on NVIDIA RTX 5000 and V100, respectively, over the state-of-the-art GPU Huffman encoder, and by up to 3.3x over the multi-thread encoder on two 28-core Xeon Platinum 8280 CPUs.