The Reverse Cuthill-McKee Algorithm in Distributed-Memory

Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering methods such as nested dissection, many important ordering methods have not been efficiently mapped to distributed-memory architectures. In this paper, we present the first-ever distributed-memory implementation of the reverse Cuthill-McKee (RCM) algorithm for reducing the profile of a sparse matrix. Our parallelization uses a two-dimensional sparse matrix decomposition. We achieve high performance by decomposing the problem into a small number of primitives and utilizing optimized implementations of these primitives. Our implementation shows strong scaling up to 1024 cores for smaller matrices and up to 4096 cores for larger matrices

An Empirical Evaluation of Allgatherv on Multi-GPU Systems

Applications for deep learning and big data analytics have compute and memory requirements that exceed the limits of a single GPU. However, effectively scaling out an application to multiple GPUs is challenging due to the complexities of communication between the GPUs, particularly for collective communication with irregular message sizes. In this work, we provide a performance evaluation of the Allgatherv routine on multi-GPU systems, focusing on GPU network topology and the communication library used. We present results from the OSU-micro benchmark as well as conduct a case study for sparse tensor factorization, one application that uses Allgatherv with highly irregular message sizes. We extend our existing tensor factorization tool to run on systems with different node counts and varying number of GPUs per node. We then evaluate the communication performance of our tool when using traditional MPI, CUDA-aware MVAPICH and NCCL across a suite of real-world data sets on three different systems: a 16-node cluster with one GPU per node, NVIDIA's DGX-1 with 8 GPUs and Cray's CS-Storm with 16 GPUs. Our results show that irregularity in the tensor data sets produce trends that contradict those in the OSU micro-benchmark, as well as trends that are absent from the benchmark.Comment: 2018 18th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID