===================================================================
RCS file: /home/cvs/OpenXM/doc/issac2000/homogeneous-network.tex,v
retrieving revision 1.8
retrieving revision 1.13
diff -u -p -r1.8 -r1.13
--- OpenXM/doc/issac2000/homogeneous-network.tex	2000/01/16 03:15:49	1.8
+++ OpenXM/doc/issac2000/homogeneous-network.tex	2000/01/17 08:50:56	1.13
@@ -1,4 +1,4 @@
-% $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 1.12 2000/01/17 08:06:15 noro Exp $
 
 \subsection{Distributed computation with homogeneous servers}
 \label{section:homog}
@@ -34,9 +34,9 @@ Figure \ref{speedup}
 shows the speedup factor under the above distributed computation
 on Risa/Asir. For each $n$, two polynomials of degree $n$
 with 3000bit coefficients are generated and the product is computed.
-The machine is Fujitsu AP3000,
-a cluster of Sun connected with a high speed network and MPI over the
-network is used to implement OpenXM.
+The machine is FUJITSU AP3000,
+a cluster of Sun workstations connected with a high speed network 
+and MPI over the network is used to implement OpenXM.
 \begin{figure}[htbp]
 \epsfxsize=8.5cm
 \epsffile{speedup.ps}
@@ -53,21 +53,22 @@ 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.
-If OpenXM provides the broadcast and the reduce operations, the cost of 
-sending $f_1$, $f_2$ and gathering $F_j$ may be reduced to $O(log_2L)$
+is not large, say, up to 10 under the above environment.
+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}