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version 1.3, 2001/06/20 02:39:25 version 1.6, 2001/06/20 03:18:21
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 % $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.2 2001/06/20 01:43:12 noro Exp $  % $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.5 2001/06/20 03:08:05 takayama 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. As the current specification of OpenXM does  with homogeneous servers.
 not include communication between servers, one cannot expect  %As the current specification of OpenXM does
 the maximal parallel speedup. However it is possible to execute  %not include communication between servers, one cannot expect
 several types of distributed computation as follows.  %the maximal parallel speedup. However it is possible to execute
   %several types of distributed computation as follows.
   
 \subsubsection{Competitive distributed computation by various strategies}  \subsubsection{Competitive distributed computation by various strategies}
   
 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.
 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 49  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 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.
   
 %\subsubsection{Nesting of client-server communication}  \subsubsection{Nesting of client-server communication}
 %  
 %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.
 %\begin{figure}  \begin{figure}
 %\label{tree}  \label{tree}
 %\begin{center}  \begin{center}
 %\begin{picture}(200,70)(0,0)  \begin{picture}(200,70)(0,0)
 %\put(70,70){\framebox(40,15){client}}  \put(70,70){\framebox(40,15){client}}
 %\put(20,30){\framebox(40,15){server}}  \put(20,30){\framebox(40,15){server}}
 %\put(70,30){\framebox(40,15){server}}  \put(70,30){\framebox(40,15){server}}
 %\put(120,30){\framebox(40,15){server}}  \put(120,30){\framebox(40,15){server}}
 %\put(0,0){\framebox(40,15){server}}  \put(0,0){\framebox(40,15){server}}
 %\put(50,0){\framebox(40,15){server}}  \put(50,0){\framebox(40,15){server}}
 %\put(150,0){\framebox(40,15){server}}  \put(150,0){\framebox(40,15){server}}
 %  
 %\put(90,70){\vector(-2,-1){43}}  \put(90,70){\vector(-2,-1){43}}
 %\put(90,70){\vector(0,-1){21}}  \put(90,70){\vector(0,-1){21}}
 %\put(90,70){\vector(2,-1){43}}  \put(90,70){\vector(2,-1){43}}
 %\put(40,30){\vector(-2,-1){22}}  \put(40,30){\vector(-2,-1){22}}
 %\put(40,30){\vector(2,-1){22}}  \put(40,30){\vector(2,-1){22}}
 %\put(140,30){\vector(2,-1){22}}  \put(140,30){\vector(2,-1){22}}
 %\end{picture}  \end{picture}
 %\caption{Tree-like structure of client-server communication}  \caption{Tree-like structure of client-server communication}
 %\end{center}  \end{center}
 %\end{figure}  \end{figure}
 %Such a computational model is useful for parallel implementation of  Such a computational model is useful for parallel implementation of
 %algorithms whose task can be divided into subtasks recursively.  algorithms whose task can be divided into subtasks recursively.
 %  
 %A typical example is {\it quicksort}, where an array to be sorted is  %A typical example is {\it quicksort}, where an array to be sorted is
 %partitioned into two sub-arrays and the algorithm is applied to each  %partitioned into two sub-arrays and the algorithm is applied to each
 %sub-array. In each level of recursion, two subtasks are generated  %sub-array. In each level of recursion, two subtasks are generated
Line 132  def dgr(G,V,Mod,O)
Line 131  def dgr(G,V,Mod,O)
 %}  %}
 %\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
 %a randomly generated polynomial as a {\it separator}.  a randomly generated polynomial as a {\it separator}.
 %We can apply the following simple parallelization:  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  one is sent to another server and the other factor is factorized on the server
 %itself.  itself.
 %\begin{verbatim}  %\begin{verbatim}
 %/* factorization of F */  %/* factorization of F */
 %/* E = degree of irreducible factors in F */  %/* E = degree of irreducible factors in F */
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