Communication-avoiding algorithms for linear algebra and beyond

Algorithms have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technologica...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:2013 IEEE 27th International Symposium on Parallel and Distributed Processing S. 585
1. Verfasser: Demmel, James
Format: Tagungsbericht
Sprache:Englisch
Japanisch
Veröffentlicht: IEEE 01.05.2013
Schlagworte:
Abstracts
Algorithm design and analysis
Arrays
Distributed processing
Educational institutions
Linear algebra
ISBN:146736066X, 9781467360661
ISSN:1530-2075
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Algorithms have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are linear functions of the loop indices.
ISBN:146736066X
9781467360661
ISSN:1530-2075
DOI:10.1109/IPDPS.2013.123