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version 1.6, 2001/06/20 03:18:21 version 1.7, 2001/06/20 05:42:47
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 % $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.5 2001/06/20 03:08:05 takayama 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.  Such a distributed computation is also possible on OpenXM.
   
 \begin{verbatim}  \begin{verbatim}
Line 43  def dgr(G,V,Mod,O)
Line 43  def dgr(G,V,Mod,O)
 }  }
 \end{verbatim}  \end{verbatim}
 In the above Asir program, the client creates two servers and it requests  In the above Asir program, the client creates two servers and it requests
 Gr\"obner basis comutations by the Buchberger algorithm the $F_4$ algorithm  Gr\"obner basis computations by the Buchberger algorithm
 to the servers for the same input.  and the $F_4$ algorithm to the servers for the same input.
 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
 server is reset.  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 132  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 150  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 249  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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