OpenXM/doc/calc2000p/efficient.tex - diff

Return to efficient.tex CVS log

Up to [local] / OpenXM / doc / calc2000p

version 1.2, 2000/07/22 08:11:09

version 1.3, 2000/07/31 07:26:12

Line 1

% $OpenXM: OpenXM/doc/calc2000p/efficient.tex,v 1.1 2000/07/21 08:27:11 noro Exp $

% $OpenXM: OpenXM/doc/calc2000p/efficient.tex,v 1.2 2000/07/22 08:11:09 noro Exp $

\documentclass{slides}

\topmargin -0.5cm

\textheight 9.5in

\usepackage{color}

\usepackage{rgb}

\usepackage{graphicx}

\usepackage{epsfig}

\begin{document}

\parskip 3pt

\fbox{{\huge \color{blue} We Are Efficient}}

\fbox{\large \color{blue} Efficient Computation with OpenXM}

\vskip 2pt

{\color {red} Real speedup by parallelism}

Line 23 the product of dense univariate polynomials with 3000b

Line 26 the product of dense univariate polynomials with 3000b

\vskip 8pt

{\color{green} Algorithm}(Shoup) : FFT+Chinese Remainder

\vskip 5pt

{\color{green} Parallel computing time} : $O((n\log n)/L+n{\color{red}\log L})$\\

{\color{green} Communication cost} :\\

No collective operations : $O((n\log n)/L+n{\color{red}L})$\\

\quad $O(n{\color{red}\log L})$ with collective operations\\

($L$: number of processes, $n$: degree)

\quad $O(n{\color{red}L})$ without collective operations\\

\quad ($L$: number of processes, $n$: degree)

\vskip 8pt

\vskip 5pt

\epsfxsize=17cm

\epsffile{3k.ps}

\rightline{ {\color{red} {\tt http://www.openxm.org} }}

\end{document}