We propose Distributed Neighbor Expansion (Distributed NE), a parallel and distributed graph partitioning method that can scale to trillion-edge graphs while providing high partitioning quality. Distributed NE is based on a new heuristic, called parallel expansion, where each partition is constructed in parallel by greedily expanding its edge set from a single vertex in such a way that the increase of the vertex cuts becomes local minimal. We theoretically prove that the proposed method has the upper bound in the partitioning quality. The empirical evaluation with various graphs shows that the proposed method produces higher-quality partitions than the state-of-the-art distributed graph partitioning algorithms. The performance evaluation shows that the space efficiency of the proposed method is an order-of-magnitude better than the existing algorithms, keeping its time efficiency comparable. As a result, Distributed NE can partition a trillion-edge graph using only 256 machines within 70 minutes.

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Globalization and lean initiatives increase the vulnerabilities of the supply chains (SC), where disruptions in any plant in a supply chain network (SCN) can propagate throughout the whole SCN. Redundancy is part of the SC re-engineering to improve supply chain resilience (SCRES). This paper presents a conceptual model of an SCN using graph theory, considering the relationships between plants and materials. Based on the model, the structural redundancy of the SCN is measured, which is used to assess SCRES. This assessment approach focuses on the resilience of the SCN against disruptions. Case studies are discussed to illustrate the applicability of this model and show that increasing structural redundancy of the SCN improves SCRES against disruptions.

The sparse matrix-vector (SpMV) multiplication routine is an important building block used in many iterative algorithms for solving scientific and engineering problems. One of the main challenges of SpMV is its memory-boundedness. Although compression has been proposed previously to improve SpMV performance on CPUs, its use has not been demonstrated on the GPU because of the serial nature of many compression and decompression schemes. In this paper, we introduce a family of bit-representation-optimized (BRO) compression schemes for representing sparse matrices on GPUs. The proposed schemes, BRO-ELL, BRO-COO, and BRO-HYB, perform compression on index data and help to speed up SpMV on GPUs through reduction of memory traffic. Furthermore, we formulate a BRO-aware matrix reordering scheme as a data clustering problem and use it to increase compression ratios. With the proposed schemes, experiments show that average speedups of 1.5× compared to ELLPACK and HYB can be achieved for SpMV on GPUs.

Abstract-Stencils represent an important class of computations that are used in many scientific disciplines. Increasingly, many of the stencil computations in scientific applications are being offloaded to GPUs to improve running times. Since a large part of the simulation time is spent inside the stencil kernels, optimizing the kernel is therefore important in the context of achieving greater computation efficiencies and reducing simulation time. In this work, we proposed a novel in-plane method for stencil computations on GPUs and compared its performance with the conventional method implemented in the Nvidia SDK. We also implemented an auto-tuning framework for our method to select the optimal parameters for different GPU architectures. A performance model was developed for our proposed method, and is used to speed up the auto-tuning process. Our results show that a speedup of nearly 2× can be achieved compared to Nvidia's implementation.