===================================================================
RCS file: /home/cvs/OpenXM/doc/ascm2001p/homogeneous-network.tex,v
retrieving revision 1.2
retrieving revision 1.8
diff -u -p -r1.2 -r1.8
--- OpenXM/doc/ascm2001p/homogeneous-network.tex	2001/06/20 01:43:12	1.2
+++ OpenXM/doc/ascm2001p/homogeneous-network.tex	2001/06/21 03:09:46	1.8
@@ -1,19 +1,57 @@
-% $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.1 2001/06/19 07:32:58 noro Exp $
+% $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.7 2001/06/20 05:42:47 takayama Exp $
 
 \subsection{Distributed computation with homogeneous servers}
 \label{section:homog}
 
 One of the aims of OpenXM is a parallel speedup by a distributed computation
-with homogeneous servers. As the current specification of OpenXM does
-not include communication between servers, one cannot expect
-the maximal parallel speedup. However it is possible to execute
-several types of distributed computation as follows.
+with homogeneous servers.  Let us see some examples.
+%As the current specification of OpenXM does
+%not include communication between servers, one cannot expect
+%the maximal parallel speedup. However it is possible to execute
+%several types of distributed computation as follows.
 
+\subsubsection{Competitive distributed computation by various strategies}
+
+SINGULAR \cite{Singular} implements MP interface for distributed
+computation and a competitive Gr\"obner basis computation is
+illustrated as an example of distributed computation by the interface.
+Such a distributed computation is also possible on OpenXM.
+
+\begin{verbatim}
+extern Proc1,Proc2$
+Proc1 = -1$ Proc2 = -1$
+/* G:set of polys; V:list of variables */
+/* Mod: the Ground field GF(Mod); O:type of order */
+def dgr(G,V,Mod,O)
+{
+  /* invoke servers if necessary */
+  if ( Proc1 == -1 ) Proc1 = ox_launch();
+  if ( Proc2 == -1 ) Proc2 = ox_launch();
+  P = [Proc1,Proc2];
+  map(ox_reset,P); /* reset servers */
+  /* P0 executes Buchberger algorithm over GF(Mod) */
+  ox_cmo_rpc(P[0],"dp_gr_mod_main",G,V,0,Mod,O);
+  /* P1 executes F4 algorithm over GF(Mod) */
+  ox_cmo_rpc(P[1],"dp_f4_mod_main",G,V,Mod,O);
+  map(ox_push_cmd,P,262); /* 262 = OX_popCMO */
+  F = ox_select(P); /* wait for data */
+  /* F[0] is a server's id which is ready */
+  R = ox_get(F[0]);
+  if ( F[0] == P[0] ) { Win = "Buchberger"; Lose = P[1]; }
+  else { Win = "F4"; Lose = P[0]; }
+  ox_reset(Lose); /* reset the loser */
+  return [Win,R];
+}
+\end{verbatim}
+In the above Asir program, the client creates two servers and it requests 
+Gr\"obner basis computations by the Buchberger algorithm 
+and the $F_4$ algorithm to the servers for the same input.
+The client watches the streams by {\tt ox\_select()}
+and the result which is returned first is taken. Then the remaining
+server is reset.
+
 \subsubsection{Nesting of client-server communication}
 
-Under OpenXM-RFC 100 an OpenXM server can be a client of other servers.
-Figure \ref{tree} illustrates a tree-like structure of an OpenXM
-client-server communication.
 \begin{figure}
 \label{tree}
 \begin{center}
@@ -36,6 +74,12 @@ client-server communication.
 \caption{Tree-like structure of client-server communication}
 \end{center}
 \end{figure}
+%%Prog:  load ("dfff"); df_demo();  enter 100.
+Under OpenXM-RFC 100 an OpenXM server can be a client of other servers.
+%Figure \ref{tree}
+Figure 2
+illustrates a tree-like structure of an OpenXM
+client-server communication.
 Such a computational model is useful for parallel implementation of
 algorithms whose task can be divided into subtasks recursively.  
 
@@ -90,15 +134,15 @@ algorithms whose task can be divided into subtasks rec
 %  }
 %}
 %\end{verbatim}
-
+%
 A typical example is a parallelization of the Cantor-Zassenhaus
-algorithm for polynomial factorization over finite fields.
+algorithm for polynomial factorization over finite fields,
 which is a recursive algorithm.
 At each level of the recursion, a given polynomial can be
 divided into two non-trivial factors with some probability by using 
 a randomly generated polynomial as a {\it separator}.
 We can apply the following simple parallelization:
-When two non-trivial factors are generated on a server,
+when two non-trivial factors are generated on a server,
 one is sent to another server and the other factor is factorized on the server
 itself. 
 %\begin{verbatim}
@@ -110,7 +154,7 @@ itself. 
 %  if ( N == E ) return [F];
 %  M = field_order_ff(); K = idiv(N,E); L = [F];
 %  while ( 1 ) {
-%    /* gererate a random polynomial */
+%    /* generate a random polynomial */
 %    W = monic_randpoly_ff(2*E,V);
 %    /* compute a power of the random polynomial */
 %    T = generic_pwrmod_ff(W,F,idiv(M^E-1,2));
@@ -209,7 +253,7 @@ work well on OpenXM.
 %Such a distributed computation is also possible on OpenXM as follows:
 %
 %The client creates two servers and it requests 
-%Gr\"obner basis comutations from the homogenized input and the input itself
+%Gr\"obner basis computations from the homogenized input and the input itself
 %to the servers.
 %The client watches the streams by {\tt ox\_select()}
 %and the result which is returned first is taken. Then the remaining