Commit 576975ca authored by Pedro Gonnet's avatar Pedro Gonnet
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cleaned up section 3.2.

parent b142eb83
......@@ -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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