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Computing, Networking, Storage and Analysis
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SCHEDULE: NOV 15-20, 2015

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STS-k: A Multilevel Sparse Triangular Solution Scheme for NUMA Multicores

SESSION: Linear Algebra


EVENT TAG(S): Algorithms, Scientific Computing, Solvers

TIME: 4:30PM - 5:00PM

SESSION CHAIR(S): Gabriel Tanase

AUTHOR(S):Humayun Kabir, Joshua D. Booth, Guillaume Aupy, Anne Benoit, Yves Robert, Padma Raghavan



We consider techniques to improve the performance of parallel sparse triangular solution on non-uniform memory architecture multicores by extending earlier coloring and level set schemes for single-core multiprocessors. We develop STS-k, where k represents a small number of transformations for latency reduction from increased spatial and temporal locality of data accesses. We propose a graph model of data reuse to inform the development of STS-k and to prove that computing an optimal cost schedule is NP-complete. We observe significant speed-ups with STS-3 on a 32-core Intel Westmere-Ex. Execution times are reduced on average by a factor of 6 (83%) for STS-3 with coloring compared to a reference implementation using level sets. Incremental gains solely from the k level transformations in STS-k correspond to reductions in execution times by factors of 1.4 (28%) and 2 (50%) respectively, relative to reference implementations with level sets and coloring.

Chair/Author Details:

Gabriel Tanase (Chair) - IBM Corporation|

Humayun Kabir - Pennsylvania State University

Joshua D. Booth - Sandia National Laboratories

Guillaume Aupy - ENS Lyon

Anne Benoit - ENS Lyon

Yves Robert - ENS Lyon

Padma Raghavan - Pennsylvania State University

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Paper provided by the ACM Digital Library

Paper also available from IEEE Computer Society