% $OpenXM: OpenXM/doc/calc2000p/efficient.tex,v 1.3 2000/07/31 07:26:12 noro Exp $
\documentclass{slides}
\topmargin -0.5cm
\textheight 9.5in
\usepackage{color}
\usepackage{rgb}
\usepackage{graphicx}
\usepackage{epsfig}
\begin{document}
\parskip 3pt
\fbox{\large \color{blue} Efficient Computation with OpenXM}
\vskip 2pt

{\color {red} Real speedup by parallelism}

Each process can communicate with any other process on {\color{green} MPI}

$\Rightarrow$ {\color{green} Collective operations} similar to \\
{\color{SeaGreen} MPI\_Bcast} and {\color{SeaGreen} MPI\_Reduce}

\vskip 8pt

{\color{red} An example} :
the product of dense univariate polynomials with 3000bit coefficients

\vskip 8pt
{\color{green} Algorithm}(Shoup) : FFT+Chinese Remainder
\vskip 5pt
{\color{green} Communication cost} :\\
\quad  $O(n{\color{red}\log L})$ with collective operations\\
\quad  $O(n{\color{red}L})$ without collective operations\\
\quad ($L$: number of processes, $n$: degree)

\vskip 5pt

\epsfxsize=17cm
\epsffile{3k.ps}

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