version 1.3, 2000/01/07 06:27:55 |
version 1.4, 2000/01/11 05:17:11 |
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% $OpenXM: OpenXM/doc/issac2000/homogeneous-network.tex,v 1.2 2000/01/02 07:32:12 takayama Exp $ |
% $OpenXM: OpenXM/doc/issac2000/homogeneous-network.tex,v 1.3 2000/01/07 06:27:55 noro Exp $ |
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\section{Applications} |
\section{Applications} |
\subsection{Distributed computation with homogeneous servers} |
\subsection{Distributed computation with homogeneous servers} |
Line 53 compute $F_j$ in parallel is proportional to $1/L$, wh |
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Line 53 compute $F_j$ in parallel is proportional to $1/L$, wh |
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for sending and receiving of polynomials is proportional to $L$ |
for sending and receiving of polynomials is proportional to $L$ |
because we don't have the broadcast and the reduce |
because we don't have the broadcast and the reduce |
operations. Therefore the speedup is limited and the upper bound of |
operations. Therefore the speedup is limited and the upper bound of |
the speedup factor depends on the communication cost and the degree |
the speedup factor depends on the ratio of |
of inputs. Figure \ref{speedup} shows that |
the computational cost and the communication cost. |
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Figure \ref{speedup} shows that |
the speedup is satisfactory if the degree is large and the number of |
the speedup is satisfactory if the degree is large and the number of |
servers is not large, say, up to 10. |
servers is not large, say, up to 10 under the above envionment. |
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\subsubsection{Order counting of an elliptic curve} |
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\subsubsection{Gr\"obner basis computation by various methods} |
\subsubsection{Gr\"obner basis computation by various methods} |
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