Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hierarchical Parallel Matrix Multiplication on Large-Scale Distributed
  Memory Platforms   Matrix multiplication is a very important computation kernel both in its own
right as a building block of many scientific applications and as a popular
representative for other scientific applications. Cannon algorithm which dates
back to 1969 was the first efficient algorithm for parallel matrix
multiplication providing theoretically optimal communication cost. However this
algorithm requires a square number of processors. In the mid 1990s, the SUMMA
algorithm was introduced. SUMMA overcomes the shortcomings of Cannon algorithm
as it can be used on a non-square number of processors as well. Since then the
number of processors in HPC platforms has increased by two orders of magnitude
making the contribution of communication in the overall execution time more
significant. Therefore, the state of the art parallel matrix multiplication
algorithms should be revisited to reduce the communication cost further. This
paper introduces a new parallel matrix multiplication algorithm, Hierarchical
SUMMA (HSUMMA), which is a redesign of SUMMA. Our algorithm reduces the
communication cost of SUMMA by introducing a two-level virtual hierarchy into
the two-dimensional arrangement of processors. Experiments on an IBM BlueGene-P
demonstrate the reduction of communication cost up to 2.08 times on 2048 cores
and up to 5.89 times on 16384 cores.

34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math