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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 $

\section{Applications}

\subsection{Distributed computation with homogeneous servers}

Line 53 compute $F_j$ in parallel is proportional to $1/L$, wh

for sending and receiving of polynomials is proportional to $L$

because we don't have the broadcast and the reduce

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.

Figure \ref{speedup} shows that

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.

\subsubsection{Order counting of an elliptic curve}

\subsubsection{Gr\"obner basis computation by various methods}