A Recursive Algebraic Coloring Technique for Hardware-efficient Symmetric Sparse Matrix-vector Multiplication

Alappat C, Basermann A, Bishop AR, Fehske H, Hager G, Schenk O, Thies J, Wellein G (2020)

Publication Type: Journal article

Publication year: 2020

Journal

ACM Transactions on Parallel Computing Association for Computing Machinery (ACM)

Book Volume: 7

Article Number: 19

Journal Issue: 3

DOI: 10.1145/3399732

Abstract

The symmetric sparse matrix-vector multiplication (SymmSpMV) is an important building block for many numerical linear algebra kernel operations or graph traversal applications. Parallelizing SymmSpMV on today's multicore platforms with up to 100 cores is difficult due to the need to manage conflicting updates on the result vector. Coloring approaches can be used to solve this problem without data duplication, but existing coloring algorithms do not take load balancing and deep memory hierarchies into account, hampering scalability and full-chip performance. In this work, we propose the recursive algebraic coloring engine (RACE), a novel coloring algorithm and open-source library implementation that eliminates the shortcomings of previous coloring methods in terms of hardware efficiency and parallelization overhead. We describe the level construction, distance-k coloring, and load balancing steps in RACE, use it to parallelize SymmSpMV, and compare its performance on 31 sparse matrices with other state-of-the-art coloring techniques and Intel MKL on two modern multicore processors. RACE outperforms all other approaches substantially. By means of a parameterized roofline model, we analyze the SymmSpMV performance in detail and discuss outliers. While we focus on SymmSpMV in this article, our algorithm and software are applicable to any sparse matrix operation with data dependencies that can be resolved by distance-k coloring.

Authors with CRIS profile

Christie Alappat Regionales Rechenzentrum Erlangen (RRZE) Georg Hager Regionales Rechenzentrum Erlangen (RRZE) Gerhard Wellein Professur für Höchstleistungsrechnen

Involved external institutions

Università della Svizzera italiana (USI) CH Switzerland (CH) Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR) / German Aerospace Center DE Germany (DE) Los Alamos National Laboratory US United States (USA) (US)

How to cite

APA:

Alappat, C., Basermann, A., Bishop, A.R., Fehske, H., Hager, G., Schenk, O.,... Wellein, G. (2020). A Recursive Algebraic Coloring Technique for Hardware-efficient Symmetric Sparse Matrix-vector Multiplication. ACM Transactions on Parallel Computing, 7(3). https://dx.doi.org/10.1145/3399732

MLA:

Alappat, Christie, et al. "A Recursive Algebraic Coloring Technique for Hardware-efficient Symmetric Sparse Matrix-vector Multiplication." ACM Transactions on Parallel Computing 7.3 (2020).

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