A Recursive Algebraic Coloring Technique for Hardware-Efficient Symmetric Sparse Matrix-Vector Multiplication
Additional information
Authors
ALAPPAT C.,
Hager G.,
Schenk O.,
Thies J.,
Basermann A.,
Bishop A.,
Fehske H.,
Wellein G.
Type
Journal Article
Year
2020
Language
English
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, which 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 and behaves in accordance with the roofline model. Outliers are discussed and analyzed in detail.
Journal
ACM Transactions on Parallel Computing
Start page number
1
End page number
40
DOI
Keywords
sparse matrix, sparse symmetric matrix-vector multiplication, graph algorithms, graph coloring, scheduling, memory hierarchies
