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Schrick-Noah_MPI-Tasking.aux

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@@ -107,15 +107,15 @@
 \bibdata{Bibliography}
 \bibcite{9678822}{1}
 \bibcite{7993827}{2}
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 \bibcite{8652334}{3}
 \bibcite{baloyi_guidelines_2019}{4}
 \bibcite{allman_complying_2006}{5}
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Schrick-Noah_MPI-Tasking.log

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Schrick-Noah_MPI-Tasking.tex

@@ -23,7 +23,7 @@
 
 \begin{document}
 
-\title{Parallelization of Large-Scale Attack and Compliance Graph Generation Using Message-Passing Interface
+\title{An Algorithm for the Parallelization of Large-Scale Attack and Compliance Graph Generation Using Message-Passing Interface
 }
 
 \author{NOAH L. SCHRICK\,\orcidlink{0000-0003-0875-8927}~\IEEEmembership{Member,~IEEE,}, AND PETER J. HAWRYLAK\,\orcidlink{0000-0003-3268-7452},~\IEEEmembership{Senior Member,~IEEE,}
@@ -301,7 +301,7 @@ Exploratory data analysis was performed on the resulting data using Python to as
     \centering
     \includegraphics[width=\linewidth]{"./images/nodes-runtime.png"}
     \includegraphics[width=\linewidth]{"./images/exploits-runtime.png"}
-    \caption{Number of Nodes and Number of Exploits (Averaged) vs. Runtime (ms)}
+    \caption{Number of Nodes and Number of Exploits (Averaged) vs. Runtime (ms), Combining and Averaging Across All Other Parameters}
     \label{fig:nodes-exp}
 \end{figure}
 
@@ -309,29 +309,29 @@ Exploratory data analysis was performed on the resulting data using Python to as
     \centering
     \includegraphics[width=\linewidth]{"./images/applicability-runtime.png"}
     \includegraphics[width=\linewidth]{"./images/dbload-runtime.png"}
-    \caption{Applicability of Exploits (\%) and Database Load (\%) (Averaged) vs. Runtime (ms)}
+    \caption{Applicability of Exploits (\%) and Database Load (\%) (Averaged) vs. Runtime (ms), Combining and Averaging Across All Other Parameters}
     \label{fig:appl-load}
 \end{figure}
 
 In terms of speedup, when the number of entries in the exploit list is small, the serial approach has better performance. As discussed in Section \ref{sec:Task-perf-expec}, this is expected due to the time elapsed for the communication cost exceeding the time taken to generate a state. However, as the number of items in the exploit list increase, the Tasking Approach quickly begins to outperform the serial approach. It is notable that even when the tasking pipeline is not fully saturated (when there are less compute nodes assigned than tasks), the performance is still approximately equal to that of the serial approach. The other noticeable feature is that as more compute nodes are assigned, the speedup continues to increase.
 
-Figure \ref{fig:overall-speedup} displays the overall minimum, maximum, and mean of speedup across all problem sizes. It is observable through the mean and maximum bars that as other problem size parameters increase, the speedup of the Tasking Approach also increases. Since database load, applicability of exploits, and number of exploits all affect the runtime, increasing the problem size through any of these parameters showcases the viability of the parallelized approach. At the same time, it is worth noting that the parallelized approach is not strictly better. The minimum speedups shown in Figure \ref{fig:overall-speedup} demonstrate that for small problem sizes, the serial approach performs better due to the communication costs.
+Figure \ref{fig:overall-speedup} displays the overall minimum, maximum, and mean of speedup across all problem sizes. All parameters are combined and averaged, which leads to the high-magnitude drops in outcome variables. This effect is made more noticeable since the minimum-bound data was collected, where the large majority of data was collected using only a few nodes. It is observable through the mean and maximum bars that as other problem size parameters increase, the speedup of the Tasking Approach also increases. Since database load, applicability of exploits, and number of exploits all affect the runtime, increasing the problem size through any of these parameters showcases the viability of the parallelized approach. At the same time, it is worth noting that the parallelized approach is not strictly better. The minimum speedups shown in Figure \ref{fig:overall-speedup} demonstrate that for small problem sizes, the serial approach performs better due to the communication costs.
 
 \begin{figure}[htp]
     \centering
     \includegraphics[width=\linewidth]{"./images/overall-speedup.png"}
     \vspace{.2truein} \centerline{}
-        \caption{Minimum, Maximum, and Mean Speedup of MPI Tasking Across All Problem Sizes}
+    \caption{Minimum, Maximum, and Mean Speedup of MPI Tasking Across All Problem Sizes, Combining and Averaging Across All Parameters}
     \label{fig:overall-speedup}
 \end{figure}
 
-Figure \ref{fig:overall-efficiency} displays the overall minimum, maximum, and mean of efficiency across all problem sizes. In terms of efficiency, 2 compute nodes offer the greatest value. While the 2 compute node configuration does offer the greatest efficiency, it does not provide a speedup greater than 1.0 on any of the testing cases conducted. The results also demonstrate that an odd number of compute nodes in a fully saturated pipeline has better efficiency that an even number of compute nodes. When referring to Figure \ref{fig:node-alloc}, when there is an odd number number of compute nodes, Task 1 is allocated more nodes than Task 2. Task 1 was responsible for iterating through an increased size of the exploit list, so more nodes is advantageous in distributing the workload. However, when many exploits were not applicable, Task 2 had a lower workload. Some test cases only had 6 applicable exploits, which is a substantially lower workload for Task 2 compared to cases where Task 1 had upwards of 49,000 exploits. As the applicability of exploits increases, the disparity in efficiency for odd and even number of nodes is not present.
+Figure \ref{fig:overall-efficiency} displays the overall minimum, maximum, and mean of efficiency across all problem sizes. All parameters are combined and averaged, which leads to the high-magnitude drop in outcome variables. This effect is made more noticeable since the minimum-bound data was collected, where the large majority of data was collected using only a few nodes. In terms of efficiency, 2 compute nodes offer the greatest value. While the 2 compute node configuration does offer the greatest efficiency, it does not provide a speedup greater than 1.0 on any of the testing cases conducted. The results also demonstrate that an odd number of compute nodes in a fully saturated pipeline has better efficiency that an even number of compute nodes. When referring to Figure \ref{fig:node-alloc}, when there is an odd number number of compute nodes, Task 1 is allocated more nodes than Task 2. Task 1 was responsible for iterating through an increased size of the exploit list, so more nodes is advantageous in distributing the workload. However, when many exploits were not applicable, Task 2 had a lower workload. Some test cases only had 6 applicable exploits, which is a substantially lower workload for Task 2 compared to cases where Task 1 had upwards of 49,000 exploits. As the applicability of exploits increases, the disparity in efficiency for odd and even number of nodes is not present.
 
 \begin{figure}[htp]
     \centering
     \includegraphics[width=\linewidth]{"./images/overall-efficiency.png"}
     \vspace{.2truein} \centerline{}
-        \caption{Minimum, Maximum, and Mean Efficiency of MPI Tasking Across All Problem Sizes}
+    \caption{Minimum, Maximum, and Mean Efficiency of MPI Tasking Across All Problem Sizes, Combining and Averaging Across All Parameters}
     \label{fig:overall-efficiency}
 \end{figure}
 
@@ -341,7 +341,7 @@ Speedups and efficiencies were also computed across each parameter. Using pivot
     \centering
     \includegraphics[width=\linewidth]{"./images/exploit-speedup.png"}
     \includegraphics[width=\linewidth]{"./images/exploit-eff.png"}
-    \caption{Mean Speedup and Efficiency for the Exploit Parameter Across the Number of Compute Nodes}
+    \caption{Mean Speedup and Efficiency for the Exploit Parameter Across the Number of Compute Nodes, Combining and Averaging Across All Other Parameters}
     \label{fig:param-exploit}
 \end{figure}
 
@@ -349,7 +349,7 @@ Speedups and efficiencies were also computed across each parameter. Using pivot
     \centering
     \includegraphics[width=\linewidth]{"./images/appl-speedup.png"}
     \includegraphics[width=\linewidth]{"./images/appl-eff.png"}
-    \caption{Mean Speedup and Efficiency for the Applicability of Exploit Parameter Across the Number of Compute Nodes}
+    \caption{Mean Speedup and Efficiency for the Applicability of Exploit Parameter Across the Number of Compute Nodes, Combining and Averaging Across All Other Parameters}
     \label{fig:param-appl}
 \end{figure}