% $OpenXM: OpenXM/doc/calc2000p/efficient.tex,v 1.1 2000/07/21 08:27:11 noro Exp $
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\begin{document}
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\fbox{{\huge \color{blue} We Are Efficient}}

\noindent
{\color{red} OpenXM on MPI --- to achieve real speedup by parallelism}

A process can communicate with any other process on MPI
$\Rightarrow$ {\color{green} Collective operations}

{\color{green} ox\_bcast} broadcasts data from the root process to all other
processes.

{\color{green} ox\_collect} reduces  data of all processes in the root process.

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

{\color{green} Algorithm} : FFT + Chinese Remainder

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

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

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

\end{document}