Eugene,
you did not take into account the dispersion/dephasing between different
processes. As cluster size and the
number of instances of parallel process increase, the dispersion increases as
well, making different instances
to be a kind out of sync - not really out of sync, but just because of
different speed of execution on different nodes, delays, etc...
If you account for this, you get the result I mentioned.
Alex
----- Original Message -----
From: Eugene Loh
To: Open MPI Users
Sent: Thursday, September 09, 2010 11:32 PM
Subject: Re: [OMPI users] MPI_Reduce performance
Alex A. Granovsky wrote:
Isn't in evident from the theory of random processes and probability theory
that in the limit of infinitely
large cluster and parallel process, the probability of deadlocks with
current implementation is unfortunately
quite a finite quantity and in limit approaches to unity regardless on any
particular details of the program.
No, not at all. Consider simulating a physical volume. Each process is
assigned to some small subvolume. It updates conditions locally, but on the
surface of its simulation subvolume it needs information from "nearby"
processes. It cannot proceed along the surface until it has that neighboring
information. Its neighbors, in turn, cannot proceed until their neighbors have
reached some point. Two distant processes can be quite out of step with one
another, but only by some bounded amount. At some point, a leading process has
to wait for information from a laggard to propagate to it. All processes
proceed together, in some loose lock-step fashion. Many applications behave in
this fashion. Actually, in many applications, the synchronization is tightened
in that "physics" is made to propagate faster than neighbor-by-neighbor.
As the number of processes increases, the laggard might seem relatively
slower in comparison, but that isn't deadlock.
As the size of the cluster increases, the chances of a system component
failure increase, but that also is a different matter.
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