Subject:
REFEREE'S REPORT: C517: Automatic Determination of Matrix-Blocks
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Ulrich Ruede <Ulrich.Ruede@informatik.uni-erlangen.de>
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Geoffrey Fox <gcfpc@csit.fsu.edu>
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Referee's Report for "Concurrency and Computation:Practice and Experience"

Manuscript: C517: Automatic Determination of Matrix-Blocks
                  by: Victor Eijkhout

D: Referee Comments (For Editor Only)

I do not think the paper should be published in this form.

E: Referee Comments (For Author and Editor)

This paper deals with algorithms for the automatic determination
of structure in sparse matrices. Many - especially very large sparse
matrices arise from the discretization of partial differential equations
and therefore have an inherent structure which can be used in algorithms
like domain decomposition. Once the matric has been constructed, the
original structure is lost. This paper deals with algorithms which can
reconstruct this information given only the matrix, but no information
on where the matrix comes from.

This is potentially an important and useful problem. Though a
good interface between PDE and solver should probably pass the extra
information (like grid structure, blocks, subdomains, etc) to the  solver,
in many realistic applications this information is not available and
a black box solver must be used given only the matrix and no extra
information.

So the topic is promising, but unfortunately, the 6 page paper itself
is quite disappointing.  The algorithms are described poorly. Except a
few code fragments the description of the algorithms remains informal
and vague. I have not been able to understand what the algorithms do in
detail. The hints at their parallelization are unintelligible.

Even worse, there is hardly any attempt to discuss the properties of these
algorithms.  What is the complexity and how does it depend on the specific
matrices considered? What role play the data structures for the matrices?

Of course it would also be interesting to study the the quality of the
automatically constructed partitions and compare them to those obtained
manually for the same problem.

At least for model problems, as they arise in typical 2D and 3D
grid problems, the algorithmic complexity of the algorithms could be
analyzed. In that case, the type of partitions could be compared to those
from typical grid partitioning approaches. Such a more detailed analysis
would indeed be interesting, but the current paper does too little in that
direction.


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