Computational Aspects of GPU-accelerated Sparse Matrix-Vector Multiplication for Solving Markov Models

Annals of Computer Science and Information Systems

Karwacki

2018

Self Cite

The authors developed a GPU approach to the uniformization method for the computing transient solution of Markov models. The authors use two techniques to reduce the memory size of storing matrices. One of them is a modification of a storage sparse matrix format HYB; second is to utilize two GPU cards and the multicore CPU. The modified HYB format is suitable for sparse Markovian transition rate matrices and oversized matrices on single GPU, also improving computation performance at the same time. The use of two GPUs enables processing matrices of even bigger sizes.

Section: Introductionmentioning

confidence: 99%

An effective sparse storage scheme for GPU-enabled uniformization method

Annals of Computer Science and Information Systems

Karwacki

2018

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“…Fortunately, the Markov chains matrices are sparse matrices and there are a lot of storage schemes for such matrices [4,6]. We use a well-known format CSR (compressed sparse rows)-because we focus on the row-wise operations (S and M).…”

Section: Representation Of Matricesmentioning

confidence: 99%

Parallelization of stochastic bounds for Markov chains on multicore and manycore platforms

2018

J Supercomput

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The author demonstrates the methodology for parallelizing of finding stochastic bounds for Markov chains on multicore and manycore platforms. The stochastic bounds algorithm for Markov chains with the sparse matrices is investigated, thus needing a lot of irregular memory access. Its parallel implementations should scale across multiple threads and characterize with a high performance and performance portability between multicore and manycore platforms. The presented methods are built on the usage of two parallelization extensions of the C++ language: OpenMP and Cilk Plus. For this two extensions, we use two programming models, namely loop parallelism and task-based parallelism. The numerical experiments show the execution time of the implementations and the scalability on multicore and manycore platforms. This work provides the parallel implementations and at the same time presents an educational example of how computer science problems with irregular memory access can be implemented for high performance using OpenMP and Cilk Plus.

“…In the article [5] some computational aspects of GPU-accelerated sparse matrixvector multiplication were investigated. Particularly, sparse matrices appearing in modeling with Markovian queuing models were considered.…”

Section: Related Workmentioning

confidence: 99%

“…Moreover, the matdescra parameter which is a six-element char array containing additional information about the matrix, should be filled in. matdescra[0]-information about the matrix structure (G for general matrix); matdescra [1]-in case of a triangular matrix, the information about whether it is upper or lower triangular; matdescra [2]-the type of the main diagonal; matdescra [3]-information about the indexation type (F from one, C from zero) matdescra [4], matdescra [5]-not used, reserved for the future.…”

Section: Parallel Implementationmentioning

confidence: 99%

“…In our previous works [5,7,10,22] we have considered the numerical solution of Markov chains on different architectures: multi-core and GPUs. The novelty of this paper is a research of parallel implementations of explicit fourth-order Runge-Kutta method for sparse matrices arising from Markovian models on a new architecture, namely Intel Xeon Phi.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Explicit Fourth-Order Runge–Kutta Method on Intel Xeon Phi Coprocessor

Potiopa

2016

Int J Parallel Prog

Self Cite

This paper concerns an Intel Xeon Phi implementation of the explicit fourthorder Runge-Kutta method (RK4) for very sparse matrices with very short rows. Such matrices arise during Markovian modeling of computer and telecommunication networks. In this work an implementation based on Intel Math Kernel Library (Intel MKL) routines and the authors' own implementation, both using the CSR storage scheme and working on Intel Xeon Phi, were investigated. The implementation based on the Intel MKL library uses the high-performance BLAS and Sparse BLAS routines. In our application we focus on OpenMP style programming. We implement SpMV operation and vector addition using the basic optimizing techniques and the vectorization. We evaluate our approach in native and offload modes for various number of cores and thread allocation affinities. Both implementations (based on Intel MKL and made by the authors) were compared in respect of the time, the speedup and the performance. The numerical experiments on Intel Xeon Phi show that the performance of authors' implementation is very promising and gives a gain of up to two times compared to the multithreaded implementation (based on Intel MKL) running on CPU (Intel Xeon processor) and even three times in comparison with the application which uses Intel MKL on Intel Xeon Phi.The authors are grateful to Czestochowa University of Technology for granting access to Intel CPU and Intel Xeon Phi platforms providing by the MICLAB