figure: plan and relaxation

klinik2018-c2-planning-scheduling.tex

@@ -48,7 +48,10 @@
 \renewcommand{\IEEEproofindentspace}{0pt}
 
 \usepackage{tikz}
-\usetikzlibrary{arrows.meta}
+\usetikzlibrary{arrows}
+\usetikzlibrary{positioning}
+\usetikzlibrary{matrix}
+\usetikzlibrary{shapes}
 
 \usepackage{listings}
 \input{languages.tex}
@@ -146,6 +149,7 @@
 \tikzset{skyline/.style={very thick}}
 \tikzset{axis/.style={->}}
 \tikzset{endInterval/.style={Bracket[]-Bracket[]}}
+\tikzstyle{task}=[draw, minimum width=2em, minimum height=1.4em, text centered, inner sep=0.3em ]
 
 % https://tex.stackexchange.com/questions/49888/tikzpicture-alignment-and-centering
 \tikzset

planning.tex

@@ -199,3 +199,38 @@ This counterexample is a valid plan.
 
 
 \subsection{Plan Relaxation Using Dependence Analysis}
+
+Given a valid plan from the synthesizer, the \emph{relaxer} identifies those actions of the plan that must be executed in the given order, and removes constraints from all others.
+The relaxer uses dependence analysis, a common technique in the field of compiler construction to identify instructions that can be reordered or parallelized.
+
+\begin{example}
+(Making coffee, continued)
+\Cref{fig:makingCoffee:relaxation} shows two plans for making coffee, one as it could be output by the plan synthesizer, and one after relaxation.
+The relaxer sees that \name{AddWater} and \name{AddBeans} are independent of each other, but that \name{MakeCoffee} depends on both.
+The reason for this is that \name{AddWater} and \name{AddBeans} act on different regions of the state.
+\qed
+
+\begin{figure}
+\begin{tikzpicture}[->,>=stealth']
+\matrix[column sep=1cm]
+{
+  \node[task] (A) {AddWater}; & \node[task] (B) {AddBeans}; & \node[task] (C) {MakeCoffee}; \\
+};
+\path (A) edge (B);
+\path (B) edge (C);
+\end{tikzpicture}
+
+\begin{tikzpicture}[->,>=stealth']
+\matrix[column sep=1cm]
+{
+\node[task] (A) {AddWater}; \\
+& \node[task] (C) {MakeCoffee}; \\
+\node[task] (B) {AddBeans}; \\
+};
+\path (A) edge (C);
+\path (B) edge (C);
+\end{tikzpicture}
+\caption{The plan for making coffee, before and after relaxation. Arrows indicate dependencies.}
+\label{fig:makingCoffee:relaxation}
+\end{figure}
+\end{example}