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<H1><A NAME=SECTION04220000000000000000>10.2 Parallel Random Numbers</A></H1>
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<A NAME=14657>&#160;</A>
We can distinguish three general approaches to the generation of
<A NAME=14658>&#160;</A>
random numbers on parallel computers: centralized, replicated, and
distributed.  In the <em> centralized
 </em> approach, a sequential
generator is encapsulated in a task from which other tasks request
random numbers.  This avoids the problem of generating multiple
independent random sequences, but is unlikely to provide good
performance.  Furthermore, it makes reproducibility hard to achieve:
the response to a request depends on when it arrives at the generator,
and hence the result computed by a program can vary from one run to
the next.
<P>
In the <em> replicated
 </em> approach, multiple instances of the same
<A NAME=14661>&#160;</A>
generator are created (for example, one per task). Each generator uses
either the same seed or a unique seed, derived, for example, from a
task identifier.  Clearly, sequences generated in this fashion are not
guaranteed to be independent and, indeed, can suffer from serious
correlation problems.  However, the approach has the advantages of
efficiency and ease of implementation and should be used when
appropriate.
<P>
In the <em> distributed
 </em> approach, responsibility for generating
a single sequence is partitioned among many generators, which can then
<A NAME=14663>&#160;</A>
be parceled out to different tasks.  The generators are all derived
from a single generator; hence, the analysis of the statistical properties of
the distributed generator is simplified.  As only distributed
generators are at all difficult to implement on parallel computers, we
focus on this topic in the rest of this chapter.
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<B> Next:</B> <A NAME=tex2html3414 HREF="node119.html" tppabs="http://www.dit.hcmut.edu.vn/books/system/par_anl/node119.html">10.3 Distributed Random Generators</A>
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