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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 1.11 2000/01/17 07:15:52 noro Exp $

\subsection{Distributed computation with homogeneous servers}

\label{section:homog}

Line 53 the speedup factor depends on the ratio of

the computational cost and the communication cost for each unit operation.

Figure \ref{speedup} shows that

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 environment.

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 $O(log_2L)$

and we can expect better results in such a case.

\subsubsection{Competitive distributed computation by various strategies}

Singular \cite{Singular} implements {\tt MP} interface for distributed

SINGULAR \cite{Singular} implements {\it MP} interface for distributed

computation and a competitive Gr\"obner basis computation is

illustrated as an example of distributed computation.

Such a distributed computation is also possible on OpenXM.

The following Risa/Asir function computes a Gr\"obner basis by

starting the computations simultaneously from the homogenized input and

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.

\begin{verbatim}