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Параллельная реализация алгоритма вычислений базисов Гребнера и Жане на уровне редукции полиномов

Параллельная реализация алгоритма вычислений базисов Гребнера и Жане на уровне редукции полиномов

Abstract

In previous papers we presented algorithm for parallel calculation of Gr.obner and Janet bases that works in terms of parallel normal forms computations. The realization was quite promising but faced problem of "starvation" (e.g. in some moments of time only few processors was fully loaded). In this talk one approach to raise scalability and avoid "starvation" will be presented. Experimental results of parallel computations on eight core SMP machine will be shown. Work was partially supported by the RFBR grant 07-01-00660 and by the grant 1027.2008.2 of the Ministry of Education and Science of the Russian Federation.

В предыдущих работах был представлен алгоритм для параллельного вычисления базисов Гребнера и Жане, работающий в терминах параллельного вычисления нормальных форм. Реализация выглядела многообещающе, но столкнулась с проблемой «голодания»(т.е. в некоторые моменты времени загружено мало вычислительных ядер машины). В этой работе представлен один подход повышения масштабируемости и избежания «голодания». Представлены данные по ускорению вычислений на восьмиядерной SMP машине.

Keywords

БАЗИС ГРEБНЕРА, БАЗИС ЖАНЕ, ПАРАЛЛЕЛИЗАЦИЯ, МАСШТАБИРУЕМОСТЬ, GR.OBNER BASES

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
bronze