tree_frontier.tex

Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \draw[black!13,line width=.25pt] (0.85,0.8) -- (0.85,4);
4 \draw[] (0.85,0.74) -- (0.85,0.86);
5 \node[font=\small,align=center,font=\scriptsize] at (0.85,0.54) {0};
6 \draw[black!13,line width=.25pt] (2.696154,0.8) -- (2.696154,4);
7 \draw[] (2.696154,0.74) -- (2.696154,0.86);
8 \node[font=\small,align=center,font=\scriptsize] at (2.696154,0.54) {2};
9 \draw[black!13,line width=.25pt] (4.542308,0.8) -- (4.542308,4);
10 \draw[] (4.542308,0.74) -- (4.542308,0.86);
11 \node[font=\small,align=center,font=\scriptsize] at (4.542308,0.54) {4};
12 \draw[black!13,line width=.25pt] (6.388462,0.8) -- (6.388462,4);
13 \draw[] (6.388462,0.74) -- (6.388462,0.86);
14 \node[font=\small,align=center,font=\scriptsize] at (6.388462,0.54) {6};
15 \draw[black!13,line width=.25pt] (0.85,1.090909) -- (6.85,1.090909);
16 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.69,1.090909) {1};
17 \draw[black!13,line width=.25pt] (0.85,2.254545) -- (6.85,2.254545);
18 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.69,2.254545) {5};
19 \draw[black!13,line width=.25pt] (0.85,3.709091) -- (6.85,3.709091);
20 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.69,3.709091) {10};
21 \draw[->,line width=.6pt] (0.85,0.8) -- (6.97,0.8);
22 \draw[->,line width=.6pt] (0.85,0.8) -- (0.85,4.12);
23 \node[font=\small,align=center,font=\scriptsize] at (3.85,0.25) {error};
24 \node[font=\small,align=center,anchor=west,font=\scriptsize] at (0.85,4.4) {cost};
25 \path[fill=black] (6.388462,1.090909) circle (0.075);
26 \path[fill=black] (4.542308,2.836364) circle (0.075);
27 \path[draw,fill=white] (2.696154,3.418182) circle (0.075);
28 \path[fill=black] (2.696154,3.127273) circle (0.075);
29 \path[fill=black] (0.85,3.709091) circle (0.075);
30 \draw[dashed,black!60] plot coordinates {(0.85,3.709091) (6.388462,1.090909)};
31 \node[font=\small,align=center] at (10.1,3.6) {Budget $B=2$: cost $8$};
32 \node[font=\small,align=center] at (10.1,2.35) {Penalty optimum: root or full split};
33 \node[font=\small,align=center,font=\small] at (10.1,1) {$8+2\lambda\le1+6\lambda$\\and $8+2\lambda\le10$\\cannot both hold.};
34 \end{tikzpicture}

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