Commit 92771bba authored by msurl's avatar msurl
Browse files

update

parent 2c225d38
\section{Abstract}\raggedbottom
Maximizing photosynthetic outcomes is one of many different objectives of a plant. In this thesis we present/ examine a method to predict an optimal veneation pattern for leafs based on the minimal number of leaf cells that have to be transformed into vein cells to supply the entire leaf with nutrients and water. The model only focusses on the number of cells and disregards other aspects of the vascular system, like the vein hierarchy. To implement this model we used a special variant of the Minimum Dominating Set Problem which we implemented using Integer Linear Programming. We call this variant to model the vascular system the Minimum Connected rooted $k$-hop Dominating Set Problem. Our results show that our implementation is not capable of solving larger instances in a reasonable amount of time. In comparison to an implementation in Answer Set Programming our implementation performs worse using the instances that represent plant leafs. We present a detailled comparison between both versions and tested instances of different structure and size. We analyzed why the Integer Linear Programming implementation performes bad on the leaf graphs. The tests also revealed that on randomly generated graphs the Integer Linear Programming implementation outperformed the Answert Set Programming implemantion.
Maximizing photosynthetic outcomes is one of many different objectives of a plant. In this thesis we present and evaluate a method to predict an optimal venation pattern for leafs based on the minimal number of leaf cells that have to be transformed into vein cells to supply the entire leaf with nutrients and water. The model only focuses on the number of cells and disregards other aspects of the vascular system, like the vein hierarchy. To implement this model we used a special variant of the Minimum Dominating Set Problem which we implemented using Integer Linear Programming. We call this variant to model the vascular system the Minimum Connected rooted $k$-hop Dominating Set Problem. Our results show that our implementation is not capable of solving larger instances in a reasonable amount of time. In comparison to an implementation in Answer Set Programming our implementation performs worse using the instances that represent plant leafs. We present a detailed comparison between both versions and tested instances of different structure and size. We analyzed why the Integer Linear Programming implementation performs bad on the leaf graphs. The tests also revealed that on randomly generated graphs the Integer Linear Programming implementation outperformed the Answer Set Programming implementation.
\pagebreak
\newpage
\appendix
\section{Anhang}
\subsection*{Zusatzteil 1} \label{anhang:zusatz1}
Dies ist ein Anhang.
\newpage
\appendix
\section{Appendix}
\subsection*{Full Tables} \label{anhang:zusatz1}
\subsubsection*{ILP}
\begin{table}[H]
\centering
\begin{tabular}{l ccccccccccccc}
name & k & \# lazily added constraints & runtime(s) & optimal\\
\hline
GNM\_ 50\_ 122 & 1 & 66 & 0.034878 & 11\\
GNM\_ 50\_ 245 & 1 & 9 & 0.07 & 7\\
GNM\_ 50\_ 368 & 1 & 0 & 0.013882 & 5 \\
GNM\_ 50\_ 490 & 1 & 4 & 0.016478 & 4\\
GNM\_ 50\_ 612 & 1 & 0 & 0.017783 & 4\\
GNM\_ 50\_ 735 & 1 & 3 & 0.018471 & 3\\
GNM\_ 50\_ 858 & 1 & 3 & 0.038161 & 3\\
GNM\_ 50\_ 980 & 1 & 3 & 0.023549 & 3\\
GNM\_ 50\_ 1102 & 1 & 3 & 0.019566 & 3\\
GNM\_ 50\_ 1225 & 1 & 0 & 0.002396 & 1\\
GNM\_ 100\_ 495 & 1 & 113 & 0.376731 & 14\\
GNM\_ 100\_ 990 & 1 & 17 & 0.488522 & 8\\
GNM\_ 100\_ 1485 & 1 & 7 & 0.396982 & 6\\
GNM\_ 100\_ 1980 & 1 & 0 & 0.315584 & 5\\
GNM\_ 100\_ 2475 & 1 & 0 & 0.045136 & 4\\
GNM\_ 100\_ 2970 & 1 & 0 & 0.013737 & 3\\
GNM\_ 100\_ 3465 & 1 & 0 & 0.010702 & 3\\
GNM\_ 100\_ 3960 & 1 & 0 & 0.007955 & 2\\
GNM\_ 100\_ 4455 & 1 & 0 & 0.00505 & 2\\
GNM\_ 100\_ 4950 & 1 & 0 & 0.00535 & 1\\
GNM\_ 250\_ 3112 & 1 & 0 & 1017.303471 & [17;15]\\
GNM\_ 250\_ 6225 & 1 & 0 & 900.64 & 10 \\
GNM\_ 250\_ 9338 & 1 & 0 & 29.67 & 7\\
GNM\_ 250\_ 12450 & 1 & 0 & 46.78 & 6\\
GNM\_ 250\_ 15562 & 1 & 0 & 12.29 & 5\\
GNM\_ 250\_ 18675 & 1 & 0 & 0.97 & 4\\
GNM\_ 250\_ 21788 & 1 & 3 & 0.415836 & 3\\
GNM\_ 250\_ 24900 & 1 & 0 & 0.040482 & 3\\
GNM\_ 250\_ 28012 & 1 & 0 & 0.024473 & 2\\
GNM\_ 250\_ 31125 & 1 & 0 & 0.017227 & 1\\
GNM\_ 500\_ 12475 & 1 & 42 & 1004.920676 & [21;13]\\
GNM\_ 500\_ 24950 & 1 & 0 & 1051.277153 & [12;8]\\
GNM\_ 500\_ 37425 & 1 & 0 & 9.89 & 4\\
GNM\_ 500\_ 49900 & 1 & 0 & 1017.23594 & [6;5]\\
GNM\_ 500\_ 62375 & 1 & 0 & 178.495614 & 5\\
GNM\_ 500\_ 74850 & 1 & 0 & 9.753998 & 4\\
GNM\_ 500\_ 87325 & 1 & 0 & 21.368156 & 4\\
GNM\_ 500\_ 99800 & 1 & 0 & 0.286309 & 3\\
GNM\_ 500\_ 112275 & 1 & 0 & 0.189313 & 2\\
GNM\_ 500\_ 124750 & 1 & 0 & 0.11 & 1\\
\end{tabular}
\caption[Minimum Connected rooted $1$-hop Dominating Set Results on the random graphs]{Minimum Connected rooted $1$-hop Dominating Set Results on the random graphs}
\end{table}
\begin{table}[H]
\centering
\begin{tabular}{l cccccccccccc}
name & k & \# lazily added constraints & optimal & runtime(s)\\
\hline
GNM\_ 50\_ 122 & 2 & 67 & 11 & 0.03795\\
GNM\_ 50\_ 245 & 2 & 9 & 7 & 0.066219\\
GNM\_ 50\_ 368 & 2 & 0 & 1 & 0.008017\\
GNM\_ 50\_ 490 & 2 & 0 & 1 & 0.002605\\
GNM\_ 50\_ 612 & 2 & 0 & 1 & 0.002223\\
GNM\_ 50\_ 735 & 2 & 0 & 1 & 0.002411\\
GNM\_ 50\_ 858 & 2 & 0 & 1 & 0.002486\\
GNM\_ 50\_ 980 & 2 & 0 & 1 & 0.002173\\
GNM\_ 50\_ 1102 & 2 & 0 & 1 & 0.012025\\
GNM\_ 50\_ 1225 & 2 & 0 & 1 & 0.001756\\
GNM\_ 100\_ 495 & 2 & 6 & 4 & 0.108993\\
GNM\_ 100\_ 990 & 2 & 12 & 2 & 0.060489\\
GNM\_ 100\_ 1485 & 2 & 0 & 1 & 0.022559\\
GNM\_ 100\_ 1980 & 2 & 0 & 1 & 0.004219\\
GNM\_ 100\_ 2475 & 2 & 0 & 1 & 0.004791\\
GNM\_ 100\_ 2970 & 2 & 0 & 1 & 0.044863\\
GNM\_ 100\_ 3465 & 2 & 0 & 1 & 0.004259\\
GNM\_ 100\_ 3960 & 2 & 0 & 1 & 0.004273\\
GNM\_ 100\_ 4455 & 2 & 0 & 1 & 0.003927\\
GNM\_ 100\_ 4950 & 2 & 0 & 1 & 0.003468\\
GNM\_ 250\_ 3112 & 2 & 0 & 2 & 0.270981\\
GNM\_ 250\_ 6225 & 2 & 28 & 1 & 0.101028\\
GNM\_ 250\_ 9338 & 2 & 0 & 1 & 0.17136\\
GNM\_ 250\_ 12450 & 2 & 0 & 1 & 0.031756\\
GNM\_ 250\_ 15562 & 2 & 109 & 1 & 0.257635\\
GNM\_ 250\_ 18675 & 2 & 0 & 1 & 0.035879\\
GNM\_ 250\_ 21788 & 2 & 0 & 1 & 0.030358\\
GNM\_ 250\_ 24900 & 2 & 0 & 1 & 0.024402\\
GNM\_ 250\_ 28012 & 2 & 0 & 1 & 0.018999\\
GNM\_ 250\_ 31125 & 2 & 0 & 1 & 0.016561\\
GNM\_ 500\_ 12475 & 2 & 0 & 2 & 1.123904\\
GNM\_ 500\_ 24950 & 2 & 0 & 1 & 0.663096\\
GNM\_ 500\_ 37425 & 2 & 0 & 1 & 0.228299\\
GNM\_ 500\_ 49900 & 2 & 0 & 1 & 0.272308\\
GNM\_ 500\_ 62375 & 2 & 0 & 1 & 0.29011\\
GNM\_ 500\_ 74850 & 2 & 0 & 1 & 0.249534\\
GNM\_ 500\_ 87325 & 2 & 0 & 1 & 0.250321\\
GNM\_ 500\_ 99800 & 2 & 0 & 1 & 0.170296\\
GNM\_ 500\_ 112275 & 2 & 0 & 1 & 0.148031\\
GNM\_ 500\_ 124750 & 2 & 0 & 1 & 0.119448\\
\end{tabular}
\caption[Minimum Connected rooted $2$-hop Dominating Set Results on the random graphs]{Minimum Connected rooted $2$-hop Dominating Set Results on the random graphs}
\end{table}
\begin{table}[H]
\centering
\begin{tabular}{l cccccccccccc}
name & k & \# lazily added constraints & optimal & runtime(s)\\
\hline
GNM\_ 50\_ 122 & 3 & 0 & 2 & 0.01651\\
GNM\_ 50\_ 245 & 3 & 0 & 1 & 0.005787\\
GNM\_ 50\_ 368 & 3 & 0 & 1 & 0.007788\\
GNM\_ 50\_ 490 & 3 & 0 & 1 & 0.002089\\
GNM\_ 50\_ 612 & 3 & 0 & 1 & 0.002541\\
GNM\_ 50\_ 735 & 3 & 0 & 1 & 0.00202\\
GNM\_ 50\_ 858 & 3 & 0 & 1 & 0.001855\\
GNM\_ 50\_ 980 & 3 & 0 & 1 & 0.00213\\
GNM\_ 50\_ 1102 & 3 & 0 & 1 & 0.012196\\
GNM\_ 50\_ 1225 & 3 & 0 & 1 & 0.001661\\
GNM\_ 100\_ 495 & 3 & 0 & 1 & 0.026969\\
GNM\_ 100\_ 990 & 3 & 0 & 1 & 0.022669\\
GNM\_ 100\_ 1485 & 3 & 0 & 1 & 0.022822\\
GNM\_ 100\_ 1980 & 3 & 0 & 1 & 0.004204\\
GNM\_ 100\_ 2475 & 3 & 0 & 1 & 0.006448\\
GNM\_ 100\_ 2970 & 3 & 0 & 1 & 0.044946\\
GNM\_ 100\_ 3465 & 3 & 0 & 1 & 0.004356\\
GNM\_ 100\_ 3960 & 3 & 0 & 1 & 0.004163\\
GNM\_ 100\_ 4455 & 3 & 0 & 1 & 0.004094\\
GNM\_ 100\_ 4950 & 3 & 0 & 1 & 0.003533\\
GNM\_ 250\_ 3112 & 3 & 14 & 1 & 0.141794\\
GNM\_ 250\_ 6225 & 3 & 28 & 1 & 0.106819\\
GNM\_ 250\_ 9338 & 3 & 51 & 1 & 0.205765\\
GNM\_ 250\_ 12450 & 3 & 82 & 1 & 0.03714\\
GNM\_ 250\_ 15562 & 3 & 109 & 1 & 0.267159\\
GNM\_ 250\_ 18675 & 3 & 0 & 1 & 0.036207\\
GNM\_ 250\_ 21788 & 3 & 0 & 1 & 0.042911\\
GNM\_ 250\_ 24900 & 3 & 0 & 1 & 0.038669\\
GNM\_ 250\_ 28012 & 3 & 0 & 1 & 0.023179\\
GNM\_ 250\_ 31125 & 3 & 0 & 1 & 0.020695\\
GNM\_ 500\_ 12475 & 3 & 0 & 1 & 0.634489\\
GNM\_ 500\_ 24950 & 3 & 68 & 1 & 0.947696\\
GNM\_ 500\_ 37425 & 3 & 118 & 1 & 0.288719\\
GNM\_ 500\_ 49900 & 3 & 0 & 1 & 0.405276\\
GNM\_ 500\_ 62375 & 3 & 0 & 1 & 0.544754\\
GNM\_ 500\_ 74850 & 3 & 0 & 1 & 0.265611\\
GNM\_ 500\_ 87325 & 3 & 0 & 1 & 0.270045\\
GNM\_ 500\_ 99800 & 3 & 0 & 1 & 0.404701\\
GNM\_ 500\_ 112275 & 3 & 0 & 1 & 0.205316\\
GNM\_ 500\_ 124750 & 3 & 0 & 1 & 0.225787\\
\end{tabular}
\caption[Minimum Connected rooted $3$-hop Dominating Set Results on the random graphs]{Minimum Connected rooted $3$-hop Dominating Set Results on the random graphs}
\end{table}
\subsubsection*{ASP}
\begin{table}[H]
\centering
\begin{tabular}{l ccccccccccccc}
name & k & runtime(s) & optimal\\
\hline
GNM\_ 50\_ 122 & 1 & 0.014 & 11\\
GNM\_ 50\_ 245 & 1 & 0.033 & 7\\
GNM\_ 50\_ 368 & 1 & 0.031 & 5 \\
GNM\_ 50\_ 490 & 1 & 0.050 & 4\\
GNM\_ 50\_ 612 & 1 & 0.055 & 4\\
GNM\_ 50\_ 735 & 1 & 0.044 & 3\\
GNM\_ 50\_ 858 & 1 & 0.050 & 3\\
GNM\_ 50\_ 980 & 1 & 0.059 & 2\\
GNM\_ 50\_ 1102 & 1 & 0.052 & 3\\
GNM\_ 50\_ 1225 & 1 & 0.055 & 1\\
GNM\_ 100\_ 495 & 1 & 32.451 & 14\\
GNM\_ 100\_ 990 & 1 & 278.296 & 8\\
GNM\_ 100\_ 1485 & 1 & 42.545 & 6\\
GNM\_ 100\_ 1980 & 1 & 4.049 & 6\\
GNM\_ 100\_ 2475 & 1 & 0.655 & 4\\
GNM\_ 100\_ 2970 & 1 & 0.226 & 3\\
GNM\_ 100\_ 3465 & 1 & 0.208 & 3\\
GNM\_ 100\_ 3960 & 1 & 0.234 & 2\\
GNM\_ 100\_ 4455 & 1 & 0.253 & 2 \\
GNM\_ 100\_ 4950 & 1 & 0.246 & 1\\
GNM\_ 250\_ 3112 & 1 & 1017.204 & [23;9]\\
GNM\_ 250\_ 6225 & 1 & 1009.124 & [12;6] \\
GNM\_ 250\_ 9338 & 1 & 1009.402 & [8;5]\\
GNM\_ 250\_ 12450 & 1 & 1013.976 & [6;4]\\
GNM\_ 250\_ 15562 & 1 & 1008.099 & [5;4]\\
GNM\_ 250\_ 18675 & 1 & 25.687 & 4\\
GNM\_ 250\_ 21788 & 1 & 1.749 & 3\\
GNM\_ 250\_ 24900 & 1 & 1.830 & 3\\
GNM\_ 250\_ 28012 & 1 & 3.400 & 2\\
GNM\_ 250\_ 31125 & 1 & 1.651 & 1\\
GNM\_ 500\_ 12475 & 1 & 1016.396 & [29;7]\\
GNM\_ 500\_ 24950 & 1 & 1011.967 & [15;4]\\
GNM\_ 500\_ 37425 & 1 & 1010.582 & [10;4]\\
GNM\_ 500\_ 49900 & 1 & 1007.821 & [7;4]\\
GNM\_ 500\_ 62375 & 1 & 1006.141 & [6;4]\\
GNM\_ 500\_ 74850 & 1 & 597.053 & 4\\
GNM\_ 500\_ 87325 & 1 & 621.053 & 4\\
GNM\_ 500\_ 99800 & 1 & 13.348 & 3\\
GNM\_ 500\_ 112275 & 1 & 8.705 & 2\\
GNM\_ 500\_ 124750 & 1 & 8.058 & 1\\
\end{tabular}
\caption[Minimum Connected rooted $1$-hop Dominating Set Results on the random graphs using ASP]{Minimum Connected rooted $1$-hop Dominating Set Results on the random graphs using ASP}
\end{table}
\begin{table}[H]
\centering
\begin{tabular}{l cccccccccccc}
name & k & optimal & runtime(s)\\
\hline
GNM\_ 50\_ 122 & 2 & 5 & 0.025\\
GNM\_ 50\_ 245 & 2 & 1 & 0.030\\
GNM\_ 50\_ 368 & 2 & 1 & 0.036\\
GNM\_ 50\_ 490 & 2 & 1 & 0.036\\
GNM\_ 50\_ 612 & 2 & 1 & 0.038\\
GNM\_ 50\_ 735 & 2 & 1 & 0.046\\
GNM\_ 50\_ 858 & 2 & 1 & 0.047\\
GNM\_ 50\_ 980 & 2 & 1 & 0.049\\
GNM\_ 50\_ 1102 & 2 & 1 & 0.052\\
GNM\_ 50\_ 1225 & 2 & 1 & 0.048\\
GNM\_ 100\_ 495 & 2 & 4 & 0.084\\
GNM\_ 100\_ 990 & 2 & 2 & 0.098\\
GNM\_ 100\_ 1485 & 2 & 1 & 0.111\\
GNM\_ 100\_ 1980 & 2 & 1 & 0.143\\
GNM\_ 100\_ 2475 & 2 & 1 & 0.151\\
GNM\_ 100\_ 2970 & 2 & 1 & 0.174\\
GNM\_ 100\_ 3465 & 2 & 1 & 0.188\\
GNM\_ 100\_ 3960 & 2 & 1 & 0.206\\
GNM\_ 100\_ 4455 & 2 & 1 & 0.220\\
GNM\_ 100\_ 4950 & 2 & 1 & 0.213\\
GNM\_ 250\_ 3112 & 2 & 2 & 0.521\\
GNM\_ 250\_ 6225 & 2 & 1 & 0.652\\
GNM\_ 250\_ 9338 & 2 & 1 & 0.737\\
GNM\_ 250\_ 12450 & 2 & 1 & 0.867\\
GNM\_ 250\_ 15562 & 2 & 1 & 0.972\\
GNM\_ 250\_ 18675 & 2 & 1 & 1.141\\
GNM\_ 250\_ 21788 & 2 & 1 & 1.221\\
GNM\_ 250\_ 24900 & 2 & 1 & 1.305\\
GNM\_ 250\_ 28012 & 2 & 1 & 1.453\\
GNM\_ 250\_ 31125 & 2 & 1 & 1.519\\
GNM\_ 500\_ 12475 & 2 & 2 & 2.314\\
GNM\_ 500\_ 24950 & 2 & 1 & 2.770\\
GNM\_ 500\_ 37425 & 2 & 1 & 3.236\\
GNM\_ 500\_ 49900 & 2 & 1 & 3.702\\
GNM\_ 500\_ 62375 & 2 & 1 & 4.218\\
GNM\_ 500\_ 74850 & 2 & 1 & 4.799\\
GNM\_ 500\_ 87325 & 2 & 1 & 5.456\\
GNM\_ 500\_ 99800 & 2 & 1 & 6.199\\
GNM\_ 500\_ 112275 & 2 & 1 & 6.268\\
GNM\_ 500\_ 124750 & 2 & 1 & 6.522\\
\end{tabular}
\caption[Minimum Connected rooted $2$-hop Dominating Set Results on the random graphs using ASP]{Minimum Connected rooted $2$-hop Dominating Set Results on the random graphs using ASP}
\end{table}
\begin{table}[H]
\centering
\begin{tabular}{l cccccccccccc}
name & k & optimal & runtime(s)\\
\hline
GNM\_ 50\_ 122 & 3 & 2 & 0.022\\
GNM\_ 50\_ 245 & 3 & 1 & 0.029\\
GNM\_ 50\_ 368 & 3 & 1 & 0.032\\
GNM\_ 50\_ 490 & 3 & 1 & 0.039\\
GNM\_ 50\_ 612 & 3 & 1 & 0.041\\
GNM\_ 50\_ 735 & 3 & 1 & 0.040\\
GNM\_ 50\_ 858 & 3 & 1 & 0.041\\
GNM\_ 50\_ 980 & 3 & 1 & 0.048\\
GNM\_ 50\_ 1102 & 3 & 1 & 0.051\\
GNM\_ 50\_ 1225 & 3 & 1 & 0.053\\
GNM\_ 100\_ 495 & 3 & 1 & 0.082\\
GNM\_ 100\_ 990 & 3 & 1 & 0.101s\\
GNM\_ 100\_ 1485 & 3 & 1 & 0.119\\
GNM\_ 100\_ 1980 & 3 & 1 & 0.140\\
GNM\_ 100\_ 2475 & 3 & 1 & 0.163\\
GNM\_ 100\_ 2970 & 3 & 1 & 0.172\\
GNM\_ 100\_ 3465 & 3 & 1 & 0.186\\
GNM\_ 100\_ 3960 & 3 & 1 & 0.214\\
GNM\_ 100\_ 4455 & 3 & 1 & 0.227\\
GNM\_ 100\_ 4950 & 3 & 1 & 0.223\\
GNM\_ 250\_ 3112 & 3 & 1 & 0.529\\
GNM\_ 250\_ 6225 & 3 & 1 & 0.657\\
GNM\_ 250\_ 9338 & 3 & 1 & 0.782\\
GNM\_ 250\_ 12450 & 3 & 1 & 0.885\\
GNM\_ 250\_ 15562 & 3 & 1 & 0.967\\
GNM\_ 250\_ 18675 & 3 & 1 & 1.114\\
GNM\_ 250\_ 21788 & 3 & 1 & 1.263\\
GNM\_ 250\_ 24900 & 3 & 1 & 1.323\\
GNM\_ 250\_ 28012 & 3 & 1 & 1.489\\
GNM\_ 250\_ 31125 & 3 & 1 & 1.510\\
GNM\_ 500\_ 12475 & 3 & 1 & 2.297\\
GNM\_ 500\_ 24950 & 3 & 1 & 2.714\\
GNM\_ 500\_ 37425 & 3 & 1 & 3.250\\
GNM\_ 500\_ 49900 & 3 & 1 & 3.719\\
GNM\_ 500\_ 62375 & 3 & 1 & 4.513\\
GNM\_ 500\_ 74850 & 3 & 1 & 4.786\\
GNM\_ 500\_ 87325 & 3 & 1 & 5.305\\
GNM\_ 500\_ 99800 & 3 & 1 & 5.845\\
GNM\_ 500\_ 112275 & 3 & 1 & 6.490\\
GNM\_ 500\_ 124750 & 3 & 1 & 6.802\\
\end{tabular}
\caption[Minimum Connected rooted $3$-hop Dominating Set Results on the random graphs using ASP]{Minimum Connected rooted $3$-hop Dominating Set Results on the random graphs using ASP}
\end{table}
\clearpage
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\input{discussion}
\input{conclusion}
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545.801 204.398 545.801 202 c h
545.801 202 m f*
545.801 170 m 545.801 167.602 542.199 167.602 542.199 170 c 542.199 172.398
545.801 172.398 545.801 170 c h
545.801 170 m f*
497.801 122 m 497.801 119.602 494.199 119.602 494.199 122 c 494.199 124.398
497.801 124.398 497.801 122 c h
497.801 122 m f*
513.801 138 m 513.801 135.602 510.199 135.602 510.199 138 c 510.199 140.398
513.801 140.398 513.801 138 c h
513.801 138 m f*
497.801 154 m 497.801 151.602 494.199 151.602 494.199 154 c 494.199 156.398
497.801 156.398 497.801 154 c h
497.801 154 m f*
529.801 154 m 529.801 151.602 526.199 151.602 526.199 154 c 526.199 156.398
529.801 156.398 529.801 154 c h
529.801 154 m f*
513.801 170 m 513.801 167.602 510.199 167.602 510.199 170 c 510.199 172.398
513.801 172.398 513.801 170 c h
513.801 170 m f*
497.801 186 m 497.801 183.602 494.199 183.602 494.199 186 c 494.199 188.398
497.801 188.398 497.801 186 c h
497.801 186 m f*
529.801 186 m 529.801 183.602 526.199 183.602 526.199 186 c 526.199 188.398
529.801 188.398 529.801 186 c h
529.801 186 m f*
513.801 202 m 513.801 199.602 510.199 199.602 510.199 202 c 510.199 204.398
513.801 204.398 513.801 202 c h
513.801 202 m f*
433.801 218 m 433.801 215.602 430.199 215.602 430.199 218 c 430.199 220.398
433.801 220.398 433.801 218 c h
433.801 218 m f*
465.801 218 m 465.801 215.602 462.199 215.602 462.199 218 c 462.199 220.398
465.801 220.398 465.801 218 c h
465.801 218 m f*
497.801 218 m 497.801 215.602 494.199 215.602 494.199 218 c 494.199 220.398
497.801 220.398 497.801 218 c h
497.801 218 m f*
529.801 218 m 529.801 215.602 526.199 215.602 526.199 218 c 526.199 220.398
529.801 220.398 529.801 218 c h
529.801 218 m f*
433.801 250 m 433.801 247.602 430.199 247.602 430.199 250 c 430.199 252.398
433.801 252.398 433.801 250 c h
433.801 250 m f*
433.801 282 m 433.801 279.602 430.199 279.602 430.199 282 c 430.199 284.398
433.801 284.398 433.801 282 c h
433.801 282 m f*
449.801 234 m 449.801 231.602 446.199 231.602 446.199 234 c 446.199 236.398
449.801 236.398 449.801 234 c h
449.801 234 m f*
449.801 266 m 449.801 263.602 446.199 263.602 446.199 266 c 446.199 268.398
449.801 268.398 449.801 266 c h
449.801 266 m f*
449.801 298 m 449.801 295.602 446.199 295.602 446.199 298 c 446.199 300.398
449.801 300.398 449.801 298 c h
449.801 298 m f*
465.801 250 m 465.801 247.602 462.199 247.602 462.199 250 c 462.199 252.398
465.801 252.398 465.801 250 c h
465.801 250 m f*
465.801 282 m 465.801 279.602 462.199 279.602 462.199 282 c 462.199 284.398
465.801 284.398 465.801 282 c h
465.801 282 m f*
497.801 250 m 497.801 247.602 494.199 247.602 494.199 250 c 494.199 252.398
497.801 252.398 497.801 250 c h
497.801 250 m f*
497.801 282 m 497.801 279.602 494.199 279.602 494.199 282 c 494.199 284.398
497.801 284.398 497.801 282 c h
497.801 282 m f*
513.801 234 m 513.801 231.602 510.199 231.602 510.199 234 c 510.199 236.398
513.801 236.398 513.801 234 c h
513.801 234 m f*
513.801 266 m 513.801 263.602 510.199 263.602 510.199 266 c 510.199 268.398
513.801 268.398 513.801 266 c h
513.801 266 m f*
513.801 298 m 513.801 295.602 510.199 295.602 510.199 298 c 510.199 300.398
513.801 300.398 513.801 298 c h
513.801 298 m f*
529.801 282 m 529.801 279.602 526.199 279.602 526.199 282 c 526.199 284.398
529.801 284.398 529.801 282 c h
529.801 282 m f*
529.801 250 m 529.801 247.602 526.199 247.602 526.199 250 c 526.199 252.398
529.801 252.398 529.801 250 c h
529.801 250 m f*
0.4 w
0 J
1 j
[] 0.0 d
10 M 416 138 m 480 74 l 544 138 l 544 298 l 480 362 l 416 298 l 416 170 l 496
90 l S
416 138 m 416 170 l S
432 122 m 432 314 l S
448 106 m 448 330 l S
464 90 m 464 346 l S
480 74 m 480 394 l S
496 90 m 496 346 l S
512 106 m 512 330 l S
528 122 m 528 314 l S
416 202 m 512 106 l S
528 122 m 416 234 l S
416 266 m 544 138 l S
544 170 m 416 298 l S
432 314 m 544 202 l S
544 234 m 448 330 l S
464 346 m 544 266 l S
416 266 m 496 346 l S
416 234 m 512 330 l S
416 202 m 528 314 l S
416 170 m 544 298 l S
416 138 m 544 266 l S
432 122 m 544 234 l S
448 106 m 544 202 l S
464 90 m 544 170 l S
480 74 m 544 138 l S
0 1 0 rg
483 394 m 483 390 477 390 477 394 c 477 398 483 398 483 394 c h
483 394 m f*
1 0 0 rg
483 394 m 483 390 477 390 477 394 c 477 398 483 398 483 394 c h
483 394 m f*