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version 1.5, 2001/06/20 03:08:05 version 1.7, 2001/06/20 05:42:47
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 % $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.4 2001/06/20 02:50:16 noro Exp $  % $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.6 2001/06/20 03:18:21 noro Exp $
   
 \subsection{Distributed computation with homogeneous servers}  \subsection{Distributed computation with homogeneous servers}
 \label{section:homog}  \label{section:homog}
   
 One of the aims of OpenXM is a parallel speedup by a distributed computation  One of the aims of OpenXM is a parallel speedup by a distributed computation
 with homogeneous servers.  with homogeneous servers.  Let us see some examples.
 %As the current specification of OpenXM does  %As the current specification of OpenXM does
 %not include communication between servers, one cannot expect  %not include communication between servers, one cannot expect
 %the maximal parallel speedup. However it is possible to execute  %the maximal parallel speedup. However it is possible to execute
Line 14  with homogeneous servers. 
Line 14  with homogeneous servers. 
   
 SINGULAR \cite{Singular} implements {\it MP} interface for distributed  SINGULAR \cite{Singular} implements {\it 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 by the MP interface.
 Such a distributed computation is also possible on OpenXM as follows:  Such a distributed computation is also possible on OpenXM.
   
 The client creates two servers and it requests  
 Gr\"obner basis comutations by the Buchberger algorithm 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.  
   
 \begin{verbatim}  \begin{verbatim}
 extern Proc1,Proc2$  extern Proc1,Proc2$ Proc1 = -1$ Proc2 = -1$
 Proc1 = -1$ Proc2 = -1$  
 /* G:set of polys; V:list of variables */  /* G:set of polys; V:list of variables */
 /* Mod: the Ground field GF(Mod); O:type of order */  /* Mod: the Ground field GF(Mod); O:type of order */
 def dgr(G,V,Mod,O)  def dgr(G,V,Mod,O)
Line 50  def dgr(G,V,Mod,O)
Line 42  def dgr(G,V,Mod,O)
   return [Win,R];    return [Win,R];
 }  }
 \end{verbatim}  \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}  \subsubsection{Nesting of client-server communication}
   
   %%Prog:  load ("dfff"); df_demo();  enter 100.
 Under OpenXM-RFC 100 an OpenXM server can be a client of other servers.  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  Figure \ref{tree} illustrates a tree-like structure of an OpenXM
 client-server communication.  client-server communication.
Line 134  algorithms whose task can be divided into subtasks rec
Line 133  algorithms whose task can be divided into subtasks rec
 %\end{verbatim}  %\end{verbatim}
 %  %
 A typical example is a parallelization of the Cantor-Zassenhaus  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.  which is a recursive algorithm.
 At each level of the recursion, a given polynomial can be  At each level of the recursion, a given polynomial can be
 divided into two non-trivial factors with some probability by using  divided into two non-trivial factors with some probability by using
Line 152  itself. 
Line 151  itself. 
 %  if ( N == E ) return [F];  %  if ( N == E ) return [F];
 %  M = field_order_ff(); K = idiv(N,E); L = [F];  %  M = field_order_ff(); K = idiv(N,E); L = [F];
 %  while ( 1 ) {  %  while ( 1 ) {
 %    /* gererate a random polynomial */  %    /* generate a random polynomial */
 %    W = monic_randpoly_ff(2*E,V);  %    W = monic_randpoly_ff(2*E,V);
 %    /* compute a power of the random polynomial */  %    /* compute a power of the random polynomial */
 %    T = generic_pwrmod_ff(W,F,idiv(M^E-1,2));  %    T = generic_pwrmod_ff(W,F,idiv(M^E-1,2));
Line 251  work well on OpenXM.
Line 250  work well on OpenXM.
 %Such a distributed computation is also possible on OpenXM as follows:  %Such a distributed computation is also possible on OpenXM as follows:
 %  %
 %The client creates two servers and it requests  %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.  %to the servers.
 %The client watches the streams by {\tt ox\_select()}  %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
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