This LDRD project was a campus exec fellowship to fund (in part) Donald Nguyen’s PhD research at UT-Austin. His work has focused on parallel programming models, and scheduling irregular algorithms on shared-memory systems using the Galois framework. Galois provides a simple but powerful way for users and applications to automatically obtain good parallel performance using certain supported data containers. The naïve user can write serial code, while advanced users can optimize performance by advanced features, such as specifying the scheduling policy. Galois was used to parallelize two sparse matrix reordering schemes: RCM and Sloan. Such reordering is important in high-performance computing to obtain better data locality and thus reduce run times.
The purpose of this report is to document a basic installation of the Anasazi eigensolver package and provide a brief discussion on the numerical solution of some graph eigenvalue problems.
Krylov subspace projection methods are widely used iterative methods for solving large-scale linear systems of equations. Researchers have demonstrated that communication avoiding (CA) techniques can improve Krylov methods' performance on modern computers, where communication is becoming increasingly expensive compared to arithmetic operations. In this paper, we extend these studies by two major contributions. First, we present our implementation of a CA variant of the Generalized Minimum Residual (GMRES) method, called CAGMRES, for solving no symmetric linear systems of equations on a hybrid CPU/GPU cluster. Our performance results on up to 120 GPUs show that CA-GMRES gives a speedup of up to 2.5x in total solution time over standard GMRES on a hybrid cluster with twelve Intel Xeon CPUs and three Nvidia Fermi GPUs on each node. We then outline a domain decomposition framework to introduce a family of preconditioners that are suitable for CA Krylov methods. Our preconditioners do not incur any additional communication and allow the easy reuse of existing algorithms and software for the sub domain solves. Experimental results on the hybrid CPU/GPU cluster demonstrate that CA-GMRES with preconditioning achieve a speedup of up to 7.4x over CAGMRES without preconditioning, and speedup of up to 1.7x over GMRES with preconditioning in total solution time. These results confirm the potential of our framework to develop a practical and effective preconditioned CA Krylov method.
Scalable parallel computing is essential for processing large scale-free (power-law) graphs. The distribution of data across processes becomes important on distributed-memory computers with thousands of cores. It has been shown that two dimensional layouts (edge partitioning) can have significant advantages over traditional one-dimensional layouts. However, simple 2D block distribution does not use the structure of the graph, and more advanced 2D partitioning methods are too expensive for large graphs. We propose a new two-dimensional partitioning algorithm that combines graph partitioning with 2D block distribution. The computational cost of the algorithm is essentially the same as 1D graph partitioning. We study the performance of sparse matrix-vector multiplication (SpMV) for scale-free graphs from the web and social networks using several different partitioners and both 1D and 2D data layouts. We show that SpMV run time is reduced by exploiting the graph's structure. Contrary to popular belief, we observe that current graph and hypergraph partitioners often yield relatively good partitions on scale-free graphs. We demonstrate that our new 2D partitioning method consistently outperforms the other methods considered, for both SpMV and an eigensolver, on matrices with up to 1.6 billion nonzeros using up to 16,384 cores. Copyright 2013 ACM.