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SWIFT
SWIFTsim
Commits
576975ca
Commit
576975ca
authored
Jan 21, 2016
by
Pedro Gonnet
Browse files
cleaned up section 3.2.
parent
b142eb83
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theory/paper_pasc/pasc_paper.tex
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576975ca
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@@ -404,7 +404,8 @@ cores of a shared-memory machine \cite{gonnet2015efficient}.
\subsection
{
Task-based domain decomposition
}
Given a task-based description of a computation, partitioning it over
a fixed number of nodes is relatively straight-forward: we create
a fixed number of
{
\em
ranks
}
(using the MPI terminology)
is relatively straight-forward: we create
a
{
\em
cell hypergraph
}
in which:
\begin{itemize}
\item
Each
{
\em
node
}
represents a single cell of particles, and
...
...
@@ -416,7 +417,7 @@ two cells, the cell hypergraph is just a regular {\em cell graph}.
Any partition of the cell graph represents a partition of the
computation, i.e.~the nodes belonging to each partition each belong
to a
computational
{
\em
rank
}
(to use the MPI terminology)
, and the
to a
rank
, and the
data belonging to each cell resides on the partition/rank to which
it has been assigned.
Any task spanning cells that belong to the same partition needs only
...
...
@@ -425,19 +426,12 @@ one partition need to be evaluated on both ranks/partitions.
If we then weight each edge with the computational cost associated with
each task, then finding a
{
\em
good
}
partitioning reduces to finding a
partition of the cell graph such that:
\begin{itemize}
\item
The weight of the edges within each partition is more or less
equal, and
\item
The weight of the edges spanning two or more partitions is
minimal.
\end{itemize}
\noindent
where the first criteria provides good
{
\em
load-balancing
}
,
i.e.~each partition/rank should involve the same amount of work, and
the second criteria reduces the
{
\em
partition cost
}
, i.e.~the amount
of duplicated work between partitions/ranks
partition of the cell graph such that the maximum sum of the weight
of all edges within and spanning in a partition is minimal
(see Figure~
\ref
{
taskgraphcut
}
).
Since the sum of the weights is directly proportional to the amount
of computation per rank/partition, minimizing the maximum sum
corresponds to minimizing the time spent on the slowest rank.
Computing such a partition is a standard graph problem and several
software libraries which provide good solutions
\footnote
{
Computing
the optimal partition for more than two nodes is considered NP-hard.
}
,
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