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Introduction

The context:

This talk introduce:

2Scenarios Not all parallel implementations are adequate to all Grids.
We may have:
\begin{itemstep}
\item Parallel application developed and build a (part of a) G...
...or it
\item The Grid and implement a parallel solution suitable
\end{itemstep}

We were in the first case.

Critical factors

Aggregated metrics Frequency of Interruptions for Communication (FIC)

$\displaystyle \frac{\text{Node processing capacity (FLOPS)}*60}{\text{Total application floating point instructions}}$    

Total Time of Data Transmission (TTDT)

$\displaystyle \frac{\text{Total data to be transmitted (KB)}*8}{\text{Bandwidth of the connection (Kbps)}}$    

Aggregated metrics II Maximum Communication Overhead (MCO)

$\displaystyle = \frac{\text{TTDT (seconds)} }{\frac{1}{\text{FIC}}*60}*100$    
$\displaystyle = \frac{\text{TTDT (seconds)} * FIC}{60}*1000$    

Maximum Latency Overhead (MLO)

$\displaystyle = \frac{\text{Latency/delay}}{\text{Overall time of data transfer}}*100$    

Goodness frontier

The slope can be found through:

$\displaystyle m = \frac{A}{FIC} - \frac{TTDT}{FIC}$    

Goodness application ratio

[width=7cm]imagens/racio.eps

ECM over the grid (DISTECM)

An Elliptic Curve over a field K is the set of solutions that respect:

$\displaystyle Y^2=X^3+AX^2 + BX + C$ (1)

DISTECM:

DISTECM Assessment (grid 1 - Low-end grid)

[width=7cm]imagens/raciob.eps

DISTECM Assessment (grid 2 - Beowulf Cluster)

[width=7cm]imagens/racioc.eps

DISTECM deployment

Hardware specification:

Challenge specification:

The number P(10341) has 109 digits and was easily factored into

$\displaystyle P(10341)$ $\displaystyle = 2 * 3 * 5 * 1143831851 * C98$    

DISTECM tests

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\begin{tabularx}{\linewidth}%
{>{
\setlength{\hsize...
...criptsize No }&{\scriptsize Yes} \\ \hline
\end{tabularx}\end{center}\end{table}

[width=7cm]imagens/distecm.eps

DISTECM results

Factored C98 as:

$\displaystyle p40$ $\displaystyle = 1432602103187822193769848905472938885747$    
$\displaystyle p59$ $\displaystyle = 544049964001456954474691336991327263416950 \backslash$    
  $\displaystyle 2409607474324463$    

Using 42 hours of the SMP Dual-Xeon cluster (with 8 processors).

Future work

[b](8.6,-3.0)[width=5cm]imagens/nfsarq.eps

Conclusions

Finally:







Thank you. Questions ??







Paulo Trezentos
Paulo.Trezentos@iscte.pt
http://paulo.trezentos.gul.pt/articles/




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Paulo Treentos 2004-01-12