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Commit 3cfdc638 authored by Pedro Gonnet's avatar Pedro Gonnet
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added task-graph cut figure.

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theory/paper_pasc/pasc_paper.tex
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− 12
View file @ 3cfdc638
......@@ -349,6 +349,21 @@ the task-based approach is already more efficient than the tree-based
neighbour search on a single core, and scales efficiently to all
cores of a shared-memory machine \cite{gonnet2015efficient}.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{Figures/Hierarchy3}
\caption{Task hierarchy for the SPH computations in \swift,
including communication tasks. Arrows indicate dependencies,
i.e.~an arrow from task $A$ to task $B$ indicates that $A$
depends on $B$. The task colour corresponds to the cell or
cells it operates on, e.g.~the density and force tasks work
on individual cells or pairs of cells.
The blue cell data is on a separate rank as the yellow and
purple cells, and thus its data must be sent across during
the computation using {\tt send}/{\tt recv} tasks (diamond-shaped).}
\label{tasks}
\end{figure}
\subsection{Task-based domain decomposition}
......@@ -384,7 +399,8 @@ partition of the cell graph such that:
\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.
of duplicated work between partitions/ranks
(see Figure~\ref{taskgraphcut}).
Computing such a partition is a standard graph problem and several
software libraries which provide good solutions\footnote{Computing
......@@ -409,17 +425,17 @@ and in which communication latencies are negligible.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{Figures/Hierarchy3}
\caption{Task hierarchy for the SPH computations in \swift,
including communication tasks. Arrows indicate dependencies,
i.e.~an arrow from task $A$ to task $B$ indicates that $A$
depends on $B$. The task colour corresponds to the cell or
cells it operates on, e.g.~the density and force tasks work
on individual cells or pairs of cells.
The blue cell data is on a separate rank as the yellow and
purple cells, and thus its data must be sent across during
the computation using {\tt send}/{\tt recv} tasks (diamond-shaped).}
\label{tasks}
\includegraphics[width=0.85\columnwidth]{Figures/task_graph_cut}
\caption{Illustration of the task-based domain decomposition
in which the tasks (circles) are edges that connect one or
more resources (rectangles). The resources are partitioned
along the thick dotted line. The blue and orange tasks are
executed on the respective partitions, whereas the green
tasks along the cut line are executed on both.
The cost of this partition is the sum of the green tasks,
which are computed twice, as well as the cost imbalance
of the tasks executed in each partition.}
\label{taskgraphcut}
\end{figure}
......
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