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version 1.8, 2000/01/16 03:15:49 version 1.10, 2000/01/17 07:06:53
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 % $OpenXM: OpenXM/doc/issac2000/homogeneous-network.tex,v 1.7 2000/01/15 06:11:17 takayama Exp $  % $OpenXM: OpenXM/doc/issac2000/homogeneous-network.tex,v 1.9 2000/01/17 01:33:19 noro Exp $
   
 \subsection{Distributed computation with homogeneous servers}  \subsection{Distributed computation with homogeneous servers}
 \label{section:homog}  \label{section:homog}
Line 54  the computational cost and the communication cost for 
Line 54  the computational cost and the communication cost for 
 Figure \ref{speedup} shows that  Figure \ref{speedup} shows that
 the speedup is satisfactory if the degree is large and $L$  the speedup is satisfactory if the degree is large and $L$
 is not large, say, up to 10 under the above envionment.  is not large, say, up to 10 under the above envionment.
 If OpenXM provides the broadcast and the reduce operations, the cost of  If OpenXM provides operations for the broadcast and the reduction
   such as {\tt MPI\_Bcast} and {\tt MPI\_Reduce} respectively, the cost of
 sending $f_1$, $f_2$ and gathering $F_j$ may be reduced to $O(log_2L)$  sending $f_1$, $f_2$ and gathering $F_j$ may be reduced to $O(log_2L)$
 and we can expect better results in such a case.  and we can expect better results in such a case.
   
 \subsubsection{Competitive distributed computation by various strategies}  \subsubsection{Competitive distributed computation by various strategies}
   
 Singular \cite{Singular} implements {\tt MP} interface for distributed  SINGULAR \cite{Singular} implements {\tt MP} interface for distributed
 computation and a competitive Gr\"obner basis computation is  computation and a competitive Gr\"obner basis computation is
 illustrated as an example of distributed computation.  illustrated as an example of distributed computation.
 Such a distributed computation is also possible on OpenXM.  Such a distributed computation is also possible on OpenXM.
 The following Risa/Asir function computes a Gr\"obner basis by  The following Risa/Asir function computes a Gr\"obner basis by
 starting the computations simultaneously from the homogenized input and  starting the computations simultaneously from the homogenized input and
 the input itself.  The client watches the streams by {\tt ox\_select()}  the input itself.  The client watches the streams by {\tt ox\_select()}
 and The result which is returned first is taken. Then the remaining  and the result which is returned first is taken. Then the remaining
 server is reset.  server is reset.
   
 \begin{verbatim}  \begin{verbatim}

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