===================================================================
RCS file: /home/cvs/OpenXM/doc/issac2000/homogeneous-network.tex,v
retrieving revision 1.9
retrieving revision 1.12
diff -u -p -r1.9 -r1.12
--- OpenXM/doc/issac2000/homogeneous-network.tex	2000/01/17 01:33:19	1.9
+++ OpenXM/doc/issac2000/homogeneous-network.tex	2000/01/17 08:06:15	1.12
@@ -1,4 +1,4 @@
-% $OpenXM: OpenXM/doc/issac2000/homogeneous-network.tex,v 1.8 2000/01/16 03:15:49 noro 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}
@@ -53,14 +53,15 @@ 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 
+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.