Improving communication performance in dense linear algebra via topology aware collectives

Recent results have shown that topology aware mapping reduces network contention in communication-intensive kernels on massively parallel machines. We demonstrate that on mesh interconnects, topology aware mapping also allows for the utilization of highly-efficient topology aware collectives. We map...

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Bibliographic Details
Published in:2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC) pp. 1 - 11
Main Authors: Solomonik, Edgar, Bhatele, Abhinav, Demmel, James
Format: Conference Proceeding
Language:English
Published: New York, NY, USA ACM 12.11.2011
IEEE
Series:ACM Conferences
Subjects:
Algorithm design and analysis
Bandwidth
communication
Computing methodologies > Parallel computing methodologies > Parallel algorithms
exascale
interconnect topology
Linear algebra
mapping
Network topology
Partitioning algorithms
Theory of computation > Design and analysis of algorithms > Parallel algorithms
Three dimensional displays
Topology
interconnect topology
mapping
performance
communication
exascale
ISBN:145030771X, 9781450307710
ISSN:2167-4329
Online Access:Get full text
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Summary:Recent results have shown that topology aware mapping reduces network contention in communication-intensive kernels on massively parallel machines. We demonstrate that on mesh interconnects, topology aware mapping also allows for the utilization of highly-efficient topology aware collectives. We map novel 2.5D dense linear algebra algorithms to exploit rectangular collectives on cuboid partitions allocated by a Blue Gene/P supercomputer. Our mappings allow the algorithms to exploit optimized line multicasts and reductions. Commonly used 2D algorithms cannot be mapped in this fashion. On 16,384 nodes (65,536 cores) of Blue Gene/P, 2.5D algorithms that exploit rectangular collectives are significantly faster than 2D matrix multiplication (MM) and LU factorization, up to 8.7x and 2.1x, respectively. These speed-ups are due to communication reduction (up to 95.6% for 2.5D MM with respect to 2D MM). We also derive LogP-based novel performance models for rectangular broadcasts and reductions. Using those, we model the performance of matrix multiplication and LU factorization on a hypothetical exascale architecture.
ISBN:145030771X
9781450307710
ISSN:2167-4329
DOI:10.1145/2063384.2063487