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

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

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

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