=================================================================== RCS file: /home/cvs/OpenXM/doc/ascm2001p/homogeneous-network.tex,v retrieving revision 1.3 retrieving revision 1.4 diff -u -p -r1.3 -r1.4 --- OpenXM/doc/ascm2001p/homogeneous-network.tex 2001/06/20 02:39:25 1.3 +++ OpenXM/doc/ascm2001p/homogeneous-network.tex 2001/06/20 02:50:16 1.4 @@ -1,4 +1,4 @@ -% $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 1.3 2001/06/20 02:39:25 noro Exp $ \subsection{Distributed computation with homogeneous servers} \label{section:homog} @@ -50,36 +50,36 @@ def dgr(G,V,Mod,O) } \end{verbatim} -%\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} -%\begin{picture}(200,70)(0,0) -%\put(70,70){\framebox(40,15){client}} -%\put(20,30){\framebox(40,15){server}} -%\put(70,30){\framebox(40,15){server}} -%\put(120,30){\framebox(40,15){server}} -%\put(0,0){\framebox(40,15){server}} -%\put(50,0){\framebox(40,15){server}} -%\put(150,0){\framebox(40,15){server}} -% -%\put(90,70){\vector(-2,-1){43}} -%\put(90,70){\vector(0,-1){21}} -%\put(90,70){\vector(2,-1){43}} -%\put(40,30){\vector(-2,-1){22}} -%\put(40,30){\vector(2,-1){22}} -%\put(140,30){\vector(2,-1){22}} -%\end{picture} -%\caption{Tree-like structure of client-server communication} -%\end{center} -%\end{figure} -%Such a computational model is useful for parallel implementation of -%algorithms whose task can be divided into subtasks recursively. -% +\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} +\begin{picture}(200,70)(0,0) +\put(70,70){\framebox(40,15){client}} +\put(20,30){\framebox(40,15){server}} +\put(70,30){\framebox(40,15){server}} +\put(120,30){\framebox(40,15){server}} +\put(0,0){\framebox(40,15){server}} +\put(50,0){\framebox(40,15){server}} +\put(150,0){\framebox(40,15){server}} + +\put(90,70){\vector(-2,-1){43}} +\put(90,70){\vector(0,-1){21}} +\put(90,70){\vector(2,-1){43}} +\put(40,30){\vector(-2,-1){22}} +\put(40,30){\vector(2,-1){22}} +\put(140,30){\vector(2,-1){22}} +\end{picture} +\caption{Tree-like structure of client-server communication} +\end{center} +\end{figure} +Such a computational model is useful for parallel implementation of +algorithms whose task can be divided into subtasks recursively. + %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 %sub-array. In each level of recursion, two subtasks are generated @@ -132,16 +132,16 @@ def dgr(G,V,Mod,O) %} %\end{verbatim} % -%A typical example is a parallelization of the Cantor-Zassenhaus -%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, -%one is sent to another server and the other factor is factorized on the server -%itself. +A typical example is a parallelization of the Cantor-Zassenhaus +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, +one is sent to another server and the other factor is factorized on the server +itself. %\begin{verbatim} %/* factorization of F */ %/* E = degree of irreducible factors in F */