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Chapter4.tex

@@ -116,7 +116,7 @@ The testing information is as follows:
 \end{itemize}
 
 \TUsubsection{Results} \label{sec:Sync-Results}
-Using the testing setup described in Section \ref{sec:Sync-Test} on the platform described at the beginning of Section \ref{sec:test-platform}, results were collected in regards to the effect of synchronous firing on both state space and runtime. These results can be seen in Figures \ref{fig:Sync-RT} and \ref{fig:Sync-State}. Both figures show a decrease in the number of states and a decrease in the runtime when synchronous firing is utilized. Since synchronous firing prevents the generation of unattainable states, there is no meaningful information loss that occurs in the graphs generated with the synchronous firing feature. It is also noteworthy that even for the smallest graph generated (which only resulted in 394 states with synchronous firing enabled), the computation cost of additional work for group vectors was justified by the decrease in runtime. Since the resulting number of states was also reduced, there will be increased justification for the synchronous firing approach due to a reduced runtime for the analysis process. Further elaboration is seen in Section \ref{sec:FW}, but it is hypothesized that the synchronous firing approach will lead to an increased runtime reduction and state space reduction when more assets exist in the network due to the increased number of unattainable state permutations.
+Using the testing setup described in Section \ref{sec:Sync-Test} on the platform described at the beginning of Section \ref{sec:test-platform}, results were collected in regards to the effect of synchronous firing on both state space and runtime. These results can be seen in Figures \ref{fig:Sync-RT} and \ref{fig:Sync-State}. The respective tables are seen in Tables \ref{table:NS-Table} and \ref{table:S-Table}. Both figures show a decrease in the number of states and a decrease in the runtime when synchronous firing is utilized. Since synchronous firing prevents the generation of unattainable states, there is no meaningful information loss that occurs in the graphs generated with the synchronous firing feature. Since the resulting number of states was also reduced, there will be increased justification for the synchronous firing approach due to a reduced runtime for the analysis process. Figure \ref{fig:Sync-Spd} displays the speedup obtained when using synchronous firing instead of non-synchronous firing for identical setups. Further elaboration is seen in Section \ref{sec:FW}, but it is hypothesized that the synchronous firing approach will lead to an increased runtime reduction and state space reduction when more assets exist in the network due to the increased number of unattainable state permutations.
 
 \begin{figure} 
     \centering
@@ -134,5 +134,47 @@ Using the testing setup described in Section \ref{sec:Sync-Test} on the platform
     \label{fig:Sync-State}
 \end{figure}
 
+\begin{figure}[htp]
+    \centering
+    \includegraphics[width=\linewidth]{"./Chapter4_img/Sync_Speedup.png"}
+    \vspace{.2truein} \centerline{}
+        \caption{Speedup Obtained When Using Synchronous Firing}
+        \label{fig:Sync-Spd}
+\end{figure}
+
+\begin{table}[htp]
+    \centering
+    \begin{tabular}{|c|c|c|}
+    \hline
+        \multicolumn{3}{|c|}{Non-Synchronous Firing} \\ \hline
+        \textbf{Number of Services} & \textbf{Number of States} & \textbf{Runtime (ms)} \\ \hline
+                1                   &       37001               & 87366.65 \\ \hline
+                2                   &       46361               & 115929.97 \\ \hline
+                3                   &       72489               & 184634.34 \\ \hline
+                4                   &       93525               & 314470.16 \\ \hline
+                5                   &       209944              & 588336.01 \\ \hline
+                6                   &       423940              & 1581697.61 \\ \hline
+    \end{tabular}
+    \caption{Tabled Results for the Non-Synchronous Firing Testing}
+    \label{table:NS-Table}
+\end{table} 
+
+\begin{table}[htp]
+    \centering
+    \begin{tabular}{|c|c|c|c|}
+    \hline
+    \multicolumn{4}{|c|}{Synchronous Firing} \\ \hline
+    \textbf{Number of Services} & \textbf{Number of States} & \textbf{Runtime (ms)} & \textbf{Speedup}\\ \hline
+    1 & 6277 & 14872.86 & 5.87 \\ \hline
+        2 & 11653 & 29251.56 & 3.96 \\ \hline
+        3 & 25317 & 66799.18 & 2.76 \\ \hline
+        4 & 36949 & 102216.30 & 3.08 \\ \hline
+        5 & 83134 & 243612.05 & 2.42 \\ \hline
+        6 & 186679 & 581840.76 & 2.72 \\ \hline
+    \end{tabular}
+    \caption{Tabled Results for the Synchronous Firing Testing}
+    \label{table:S-Table}
+\end{table} 
+
 
 

Chapter5.aux

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Chapter5.tex

@@ -138,6 +138,8 @@ The results of the Tasking Approach can be seen in Figure \ref{fig:Spd-Eff-Task}
 
 In terms of efficiency, 2 compute nodes offer the greatest value since the speedup using 2 compute nodes is approximately 1.0 as the exploit list size increases. While the 2 compute node option 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. In the testing conducted, Task 1 was responsible for iterating through an increased size of the exploit list, so more nodes is advantageous in distributing the workload. However, since many exploits were not applicable, Task 2 had a lower workload where only 6 exploits could be applicable. This will be further elaborated upon in Section \ref{sec:FW}, but it is expected that efficiency will increase for real networks, since nodes in Task 2 will see a realistic workload.
 
+Figures \ref{fig:Tasking-RT}, \ref{fig:Tasking-Spd}, and \ref{fig:Tasking-Eff} display the results of the tasking approach for runtime in milliseconds, speedup, and efficiency respectively in table format.
+
 \begin{figure}[htp]
     \centering
     \includegraphics[scale=0.5]{"./Chapter5_img/NA.png"}
@@ -154,6 +156,27 @@ In terms of efficiency, 2 compute nodes offer the greatest value since the speed
     \label{fig:Spd-Eff-Task}
 \end{figure}
 
+\begin{figure}
+    \centering
+    \includegraphics[width=\linewidth]{"./Chapter5_img/Tasking_RT.png"}
+    \caption{Results for the MPI Tasking Approach in Terms of Runtime in Milliseconds}
+    \label{fig:Tasking-RT}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=\linewidth]{"./Chapter5_img/Tasking_Spd.png"}
+    \caption{Results for the MPI Tasking Approach in Terms of Speedup}
+    \label{fig:Tasking-Spd}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=\linewidth]{"./Chapter5_img/Tasking_Eff.png"}
+    \caption{Results for the MPI Tasking Approach in Terms of Efficiency}
+    \label{fig:Tasking-Eff}
+\end{figure}
+
 \TUsection{Subgraphing Approach} \label{sec:Subgraphing_Approach}
 \TUsubsection{Introduction to the Subgraphing Approach}
 As opposed to the Tasking Approach described in Section \ref{sec:Tasking-Approach}, this Section introduces the Subgraphing Approach as a means of reducing runtime by frontier distribution though subgraphing. Section \ref{sec:db-stor} discusses that the frontier is expanded at a rate faster than can be processed. This approach attempts to distribute the frontier by assigning MPI nodes a starting state, and each node will generate a subgraph up to a designated depth-limit, where each node will then return their generated subgraph to a merging process. The authors of \cite{li_concurrency_2019} presented an alternative method of frontier processing by utilizing OpenMP on a shared-memory system to assign each thread an individual state to explore that would then pass through a critical section. This approach is intended for a distributed system, and additionally differs in that each node will explore multiple states to form a subgraph, rather than exploring one individual state. This approach was implemented with two versions, and both collected results to draw conclusions in regards to speedup, efficiency, and scalability for attack graph and compliance graph generation.

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Schrick-Noah_MS-Thesis.aux

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Schrick-Noah_MS-Thesis.log

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Schrick-Noah_MS-Thesis.lot

@@ -1,3 +1,5 @@
 {\vspace {\baselineskip }}
+\contentsline {table}{\numberline {4.1}{\ignorespaces Tabled Results for the Non-Synchronous Firing Testing\relax }}{28}{}%
+\contentsline {table}{\numberline {4.2}{\ignorespaces Tabled Results for the Synchronous Firing Testing\relax }}{28}{}%
 \contentsline {table}{\numberline {5.1}{\ignorespaces MPI Tags for the MPI Tasking Approach\relax }}{39}{}%
-\contentsline {table}{\numberline {5.2}{\ignorespaces MPI Tags for the MPI Subgraphing Approach\relax }}{46}{}%
+\contentsline {table}{\numberline {5.2}{\ignorespaces MPI Tags for the MPI Subgraphing Approach\relax }}{47}{}%

Schrick-Noah_MS-Thesis.tex

@@ -128,9 +128,9 @@
 % Enter the information for the title page,
 % signature page and abstract.
 %
-\titleoneline{Generation Techniques and Message-Passing Interface Implementation for Compliance Graphs}
+\titleoneline{Compliance Graph Generation Techniques and Parallel Computing Implementations Using Message-Passing Interface}
-\title{Generation Techniques and Message-Passing Interface\\
+\title{Compliance Graph Generation Techniques and Parallel\\
-       Implementation for Compliance Graphs}  % The title with line breaks for the front pages.
+       Computing Implementations Using Message-Passing Interface}  % The title with line breaks for the front pages.
 \author{Noah L. Schrick}
 \degreename{Master of Science}
 \dept{Computer Science}

Schrick-Noah_MS-Thesis.toc

@@ -58,20 +58,20 @@
 \contentsline {subsubsection}{\numberline {5.3.2.7}MPI Tags}{38}{}%
 \contentsline {subsection}{\numberline {5.3.3}\it Performance Expectations and Use Cases}{38}{}%
 \contentsline {subsection}{\numberline {5.3.4}\it Results}{39}{}%
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+\contentsline {subsection}{\numberline {5.4.1}\it Introduction to the Subgraphing Approach}{43}{}%
-\contentsline {subsection}{\numberline {5.4.2}\it Algorithm Design}{42}{}%
+\contentsline {subsection}{\numberline {5.4.2}\it Algorithm Design}{43}{}%
-\contentsline {subsubsection}{\numberline {5.4.2.1}Worker Nodes}{43}{}%
+\contentsline {subsubsection}{\numberline {5.4.2.1}Worker Nodes}{44}{}%
-\contentsline {subsubsection}{\numberline {5.4.2.2}Root Node}{44}{}%
+\contentsline {subsubsection}{\numberline {5.4.2.2}Root Node}{45}{}%
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+\contentsline {subsubsection}{\numberline {5.4.2.3}Database Node}{46}{}%
-\contentsline {subsubsection}{\numberline {5.4.2.4}MPI Tags}{45}{}%
+\contentsline {subsubsection}{\numberline {5.4.2.4}MPI Tags}{46}{}%
-\contentsline {subsection}{\numberline {5.4.3}\it Performance Expectations and Use Cases}{45}{}%
+\contentsline {subsection}{\numberline {5.4.3}\it Performance Expectations and Use Cases}{46}{}%
-\contentsline {subsection}{\numberline {5.4.4}\it Results}{46}{}%
+\contentsline {subsection}{\numberline {5.4.4}\it Results}{47}{}%
-\contentsline {chapter}{\numberline {CHAPTER 6: }{\bf \uppercase {CONCLUSIONS AND FUTURE WORKS}}}{55}{}%
+\contentsline {chapter}{\numberline {CHAPTER 6: }{\bf \uppercase {CONCLUSIONS AND FUTURE WORKS}}}{56}{}%
-\contentsline {section}{\numberline {6.1}\bf Conclusions}{55}{}%
+\contentsline {section}{\numberline {6.1}\bf Conclusions}{56}{}%
-\contentsline {section}{\numberline {6.2}\bf Future Work}{56}{}%
+\contentsline {section}{\numberline {6.2}\bf Future Work}{57}{}%
 {\hfill \ }
-\contentsline {section}{\hspace {-\parindent }NOMENCLATURE}{59}{}%
+\contentsline {section}{\hspace {-\parindent }NOMENCLATURE}{60}{}%
 \addvspace {10pt}
-\contentsline {section}{\hspace {-\parindent }BIBLIOGRAPHY}{59}{}%
+\contentsline {section}{\hspace {-\parindent }BIBLIOGRAPHY}{60}{}%
 {\hfill \ }