Subgraphing Intro

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Chapter4.tex

@@ -89,7 +89,7 @@ The implementation of synchronous firing in the graph generation process relies
 \end{figure}
 
 
-\TUsection{Example Networks and Results}
+\TUsection{Example Networks and Results} \label{sec:test-platform}
 All data was collected on a 13 node cluster, with 12 nodes serving as dedicated compute nodes, and 1 node serving as the login node. Each compute node has a configuration as follows:
 \begin{itemize}
 \item{OS: CentOS release 6.9}
@@ -100,7 +100,7 @@ All data was collected on a 13 node cluster, with 12 nodes serving as dedicated
 \end{itemize}
 All nodes are connected with an Infiniband interconnect.
 
-\TUsubsection{Example Networks}
+\TUsubsection{Example Networks} \label{sec:Sync-Test}
 The example networks for testing the effectiveness of synchronous firing follow the compliance graph generation approach. These networks analyze two assets, both of which are identical 2006 Toyota Corolla cars with identical qualities. The generation examines both cars at their current states, and proceeds to advance in time by a pre-determined amount, up to a pre-determined limit. Each time increment updates each car by an identical amount of mileage. During the generation process, it is determined if a car is out of compliance either through mileage or time since last maintenance in accordance with the Toyota Corolla Maintenance Schedule manual.
 
 In addition, the tests employ the use of ``services", where if a car is out of compliance, it will go through a correction process and reset the mileage and time since last service. Each test varies in the number of services used. The 1 Service test only employs one service, and it is dedicated to brake pads. The 2 Service test employs two services, where the first service is dedicated to the brake pads, and the second is for exhaust pipes. This process extends to the 3 and 4 Service tests.
@@ -116,4 +116,23 @@ The testing information is as follows:
 \end{itemize}
 
 \TUsubsection{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 depict a decrease in the number of states and a decrease in the runtime when synchronous firing is leveraged. Since synchronous firing prevents the generation of illegitimate states, there is no meaningful information loss that occurs in the graphs generated from the synchronous firing method. 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 illegitimate state permutations.
+
+\begin{figure} 
+    \centering
+    \includegraphics[width=\linewidth]{"./Chapter4_img/Sync-Runtime-Bar.png"}
+    \includegraphics[width=\linewidth]{"./Chapter4_img/Sync-Runtime.png"}
+    \caption{Bar Graph and Line Graph Representations of Synchronous Firing on Runtime}
+    \label{fig:Sync-RT}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=\linewidth]{"./Chapter4_img/Sync-StateSpace-Bar.png"}
+    \includegraphics[width=\linewidth]{"./Chapter4_img/Sync-StateSpace.png"}
+    \caption{Bar Graph and Line Graph Representations of Synchronous Firing on State Space}
+    \label{fig:Sync-State}
+\end{figure}
+
+
 

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Chapter5.tex

@@ -29,7 +29,7 @@ the class instances were able to be altered with relative ease, and many of the
 did not expose enough information for the non-intrusive approach to be viable.  
 \TUsubsection{Data Consistency}
 
-\TUsection{Tasking Approach}
+\TUsection{Tasking Approach} \label{sec:Tasking-Approach}
 \TUsubsection{Introduction to the Tasking Approach}
 The high-level overview of the compliance graph generation process can be broken down into six main tasks.
 These tasks are described in Figure \ref{fig:tasks}. Prior works such as that seen by the 
@@ -96,7 +96,7 @@ Each node in Task 2 iterates through the received partial applicable exploit lis
 Task 3 is performed only by the root node, and no division of work is necessary. The root node will continuously check for new states until the Task 2 finalize signal is detected. This task consists of setting the new state's ID, adding it to the frontier, adding its information to the instance, and inserting information into the hash map. When the root node has processed all states and has received the Task 2 finalize signal, it will complete Task 3 by sending the instance and/or frontier to Task 4 and/or 5, respectively if applicable, then proceeds to Task 0.
 
 \TUsubsubsection{Task 4 and Task 5}
-Intermediate database operations, though not frequent and may never occur for small graphs, are lengthy and time-consuming when they do occur. As discussed in Section \ref{sec:db-stor}, the two main memory consumers are the frontier and the instance, both of which are contained by the root node. Since the database storage requests are blocking, the pipeline would halt for a lengthy period of time while waiting for the root node to finish potentially two large storages. Tasks 4 and 5 work to alleviate the stall by executing independently of the regular pipeline execution flow. Since Tasks 4 and 5 do not send any data, no other tasks must wait for these tasks to complete. The root node can then asynchronously send the frontier and instance to the appropriate nodes as needed, clear its memory, and continue execution without delay.
+Intermediate database operations, though not frequent and may never occur for small graphs, are lengthy and time-consuming when they do occur. As discussed in Section \ref{sec:db-stor}, the two main memory consumers are the frontier and the instance, both of which are contained by the root node. Since the database storage requests are blocking, the pipeline would halt for a lengthy period of time while waiting for the root node to finish potentially two large storages. Tasks 4 and 5 work to alleviate the stall by executing independently of the regular pipeline execution flow. Since Tasks 4 and 5 do not send any data, no other tasks must wait for these tasks to complete. The root node can then asynchronously send the frontier and instance to the appropriate nodes as needed, clear its memory, and continue execution without delay. After initial testing, it was determined that the communication cost of the asynchronous sending of data for Tasks 4 and 5 is less than the time requirement of a database storage operation performed by the root node.
 
 \TUsubsubsection{MPI Tags}
 To ensure that the intended message is received by each node, the MPI message envelopes have their tag fields specified. When a node sends a message, it specifies a tag that corresponds with the data and intent for which it is sent. The tag values were arbitrarily chosen, and tags can be added to the existing list or removed as desired. When receiving a message, a node can specify to only look for messages that have an envelope with a matching tag field. Not only do tags ensure that nodes are receiving the correct messages, they also reduce complexity for program design. Table \ref{table:tasking-tag} displays the list of tags used for the MPI Tasking approach.
@@ -131,10 +131,10 @@ To ensure that the intended message is received by each node, the MPI message en
 Due to the amount of communication between nodes to distribute the necessary data through all stages of the tasking pipeline, this approach is not expected to outperform the serial approach in all cases. This tasking approach was specifically designed to reduce the computation time when the generation of each individual state increases in time. This approach does not offer any guarantees of processing through the frontier at an increased rate; it's main objective is to distribute the workload of individual state generation. As discussed in Section \ref{sec:Intro}, the amount of entries in the National Vulnerability database and any custom vulnerability testing to ensure adequate examination of all assets in the network sums to large number of exploits in the exploit list. Likewise for compliance graphs and compliance examinations, Section \ref{sec:CG-diff} discussed that the number of compliance checks for SOX, HIPAA, GDPR, PCI DSS, and/or any other regulatory compliance also sums to a large number of exploits in the exploit list. Since the generation of each state is largely dependent on the number of exploits present in the exploit list, this approach is best-suited for when the exploit list grows in size.
 
 \TUsubsection{Results}
-Communication cost of asynchronous send for T4 and T5 is less than the time requirement of a database storage by root.
 
 \TUsection{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 it can process. 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 author 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.
 
 \TUsubsection{Algorithm Design}
 \TUsubsubsection{Communication Structure}

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-Output written on Schrick-Noah_MS-Thesis.pdf (53 pages, 599307 bytes).
+Output written on Schrick-Noah_MS-Thesis.pdf (56 pages, 822041 bytes).
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Schrick-Noah_MS-Thesis.lot

@@ -1,2 +1,2 @@
 {\vspace {\baselineskip }}
-\contentsline {table}{\numberline {5.1}{\ignorespaces MPI Tags for the MPI Tasking Approach}}{33}{}%
+\contentsline {table}{\numberline {5.1}{\ignorespaces MPI Tags for the MPI Tasking Approach\relax }}{36}{}%

Schrick-Noah_MS-Thesis.tex

@@ -91,6 +91,8 @@
 \RequirePackage{setspace}
 \usepackage{boxedminipage}
 \usepackage{graphicx}
+\usepackage{subcaption}
+
 
 % Added by Richard D Redner 2017-08-16
 % If, in the List of Tables or List of Figures, the figure/table numbers

Schrick-Noah_MS-Thesis.toc

@@ -41,57 +41,57 @@
 \contentsline {section}{\numberline {4.3}\bf Example Networks and Results}{22}{}%
 \contentsline {subsection}{\numberline {4.3.1}\it Example Networks}{22}{}%
 \contentsline {subsection}{\numberline {4.3.2}\it Results}{24}{}%
-\contentsline {chapter}{\numberline {CHAPTER 5: }{\bf \uppercase {Utilization OF MESSAGE PASSING INTERFACE}}}{25}{}%
+\contentsline {chapter}{\numberline {CHAPTER 5: }{\bf \uppercase {Utilization OF MESSAGE PASSING INTERFACE}}}{28}{}%
-\contentsline {section}{\numberline {5.1}\bf Introduction to MPI Utilization for Attack Graph Generation}{25}{}%
+\contentsline {section}{\numberline {5.1}\bf Introduction to MPI Utilization for Attack Graph Generation}{28}{}%
-\contentsline {section}{\numberline {5.2}\bf Necessary Components}{25}{}%
+\contentsline {section}{\numberline {5.2}\bf Necessary Components}{28}{}%
-\contentsline {subsection}{\numberline {5.2.1}\it Serialization}{25}{}%
+\contentsline {subsection}{\numberline {5.2.1}\it Serialization}{28}{}%
-\contentsline {subsection}{\numberline {5.2.2}\it Data Consistency}{26}{}%
+\contentsline {subsection}{\numberline {5.2.2}\it Data Consistency}{29}{}%
-\contentsline {section}{\numberline {5.3}\bf Tasking Approach}{26}{}%
+\contentsline {section}{\numberline {5.3}\bf Tasking Approach}{29}{}%
-\contentsline {subsection}{\numberline {5.3.1}\it Introduction to the Tasking Approach}{26}{}%
+\contentsline {subsection}{\numberline {5.3.1}\it Introduction to the Tasking Approach}{29}{}%
-\contentsline {subsection}{\numberline {5.3.2}\it Algorithm Design}{26}{}%
+\contentsline {subsection}{\numberline {5.3.2}\it Algorithm Design}{29}{}%
-\contentsline {subsubsection}{Communication Structure}{29}{}%
+\contentsline {subsubsection}{Communication Structure}{32}{}%
-\contentsline {subsubsection}{Task 0}{29}{}%
+\contentsline {subsubsection}{Task 0}{32}{}%
-\contentsline {subsubsection}{Task 1}{29}{}%
+\contentsline {subsubsection}{Task 1}{32}{}%
-\contentsline {subsubsection}{Task 2}{30}{}%
+\contentsline {subsubsection}{Task 2}{33}{}%
-\contentsline {subsubsection}{Task 3}{32}{}%
+\contentsline {subsubsection}{Task 3}{35}{}%
-\contentsline {subsubsection}{Task 4 and Task 5}{32}{}%
+\contentsline {subsubsection}{Task 4 and Task 5}{35}{}%
-\contentsline {subsubsection}{MPI Tags}{33}{}%
+\contentsline {subsubsection}{MPI Tags}{36}{}%
-\contentsline {subsection}{\numberline {5.3.3}\it Performance Expectations}{34}{}%
+\contentsline {subsection}{\numberline {5.3.3}\it Performance Expectations}{37}{}%
-\contentsline {subsection}{\numberline {5.3.4}\it Results}{34}{}%
+\contentsline {subsection}{\numberline {5.3.4}\it Results}{37}{}%
-\contentsline {section}{\numberline {5.4}\bf Subgraphing Approach}{34}{}%
+\contentsline {section}{\numberline {5.4}\bf Subgraphing Approach}{37}{}%
-\contentsline {subsection}{\numberline {5.4.1}\it Introduction to the Subgraphing Approach}{34}{}%
+\contentsline {subsection}{\numberline {5.4.1}\it Introduction to the Subgraphing Approach}{37}{}%
-\contentsline {subsection}{\numberline {5.4.2}\it Algorithm Design}{34}{}%
+\contentsline {subsection}{\numberline {5.4.2}\it Algorithm Design}{37}{}%
-\contentsline {subsubsection}{Communication Structure}{34}{}%
+\contentsline {subsubsection}{Communication Structure}{37}{}%
-\contentsline {subsubsection}{Worker Nodes}{34}{}%
+\contentsline {subsubsection}{Worker Nodes}{37}{}%
-\contentsline {subsubsection}{Root Node}{35}{}%
+\contentsline {subsubsection}{Root Node}{37}{}%
-\contentsline {subsubsection}{Database Node}{35}{}%
+\contentsline {subsubsection}{Database Node}{38}{}%
-\contentsline {subsection}{\numberline {5.4.3}\it Performance Expectations}{35}{}%
+\contentsline {subsection}{\numberline {5.4.3}\it Performance Expectations}{38}{}%
-\contentsline {chapter}{\numberline {CHAPTER 6: }{\bf \uppercase {PERFORMANCE ANALYSIS}}}{36}{}%
+\contentsline {chapter}{\numberline {CHAPTER 6: }{\bf \uppercase {PERFORMANCE ANALYSIS}}}{39}{}%
-\contentsline {section}{\numberline {6.1}\bf Small Networks}{36}{}%
+\contentsline {section}{\numberline {6.1}\bf Small Networks}{39}{}%
-\contentsline {subsection}{\numberline {6.1.1}\it Test Information}{36}{}%
+\contentsline {subsection}{\numberline {6.1.1}\it Test Information}{39}{}%
-\contentsline {subsection}{\numberline {6.1.2}\it Results}{36}{}%
+\contentsline {subsection}{\numberline {6.1.2}\it Results}{39}{}%
-\contentsline {subsection}{\numberline {6.1.3}\it Analysis}{36}{}%
+\contentsline {subsection}{\numberline {6.1.3}\it Analysis}{39}{}%
-\contentsline {section}{\numberline {6.2}\bf Large Networks}{36}{}%
+\contentsline {section}{\numberline {6.2}\bf Large Networks}{39}{}%
-\contentsline {subsection}{\numberline {6.2.1}\it Test Information}{36}{}%
+\contentsline {subsection}{\numberline {6.2.1}\it Test Information}{39}{}%
-\contentsline {subsection}{\numberline {6.2.2}\it Results}{36}{}%
+\contentsline {subsection}{\numberline {6.2.2}\it Results}{39}{}%
-\contentsline {subsection}{\numberline {6.2.3}\it Analysis}{36}{}%
+\contentsline {subsection}{\numberline {6.2.3}\it Analysis}{39}{}%
-\contentsline {section}{\numberline {6.3}\bf Large Exploit Lists}{36}{}%
+\contentsline {section}{\numberline {6.3}\bf Large Exploit Lists}{39}{}%
-\contentsline {subsection}{\numberline {6.3.1}\it Test Information}{36}{}%
+\contentsline {subsection}{\numberline {6.3.1}\it Test Information}{39}{}%
-\contentsline {subsection}{\numberline {6.3.2}\it Results}{36}{}%
+\contentsline {subsection}{\numberline {6.3.2}\it Results}{39}{}%
-\contentsline {subsection}{\numberline {6.3.3}\it Analysis}{36}{}%
+\contentsline {subsection}{\numberline {6.3.3}\it Analysis}{39}{}%
-\contentsline {section}{\numberline {6.4}\bf Distributed Hash Tables}{36}{}%
+\contentsline {section}{\numberline {6.4}\bf Distributed Hash Tables}{39}{}%
-\contentsline {subsection}{\numberline {6.4.1}\it Test Information}{37}{}%
+\contentsline {subsection}{\numberline {6.4.1}\it Test Information}{40}{}%
-\contentsline {subsection}{\numberline {6.4.2}\it Results}{37}{}%
+\contentsline {subsection}{\numberline {6.4.2}\it Results}{40}{}%
-\contentsline {subsection}{\numberline {6.4.3}\it Analysis}{37}{}%
+\contentsline {subsection}{\numberline {6.4.3}\it Analysis}{40}{}%
-\contentsline {chapter}{\numberline {CHAPTER 7: }{\bf \uppercase {CONCLUSIONS AND FUTURE WORKS}}}{38}{}%
+\contentsline {chapter}{\numberline {CHAPTER 7: }{\bf \uppercase {CONCLUSIONS AND FUTURE WORKS}}}{41}{}%
-\contentsline {section}{\numberline {7.1}\bf Future Work}{38}{}%
+\contentsline {section}{\numberline {7.1}\bf Future Work}{41}{}%
 {\hfill \ }
-\contentsline {section}{\hspace {-\parindent }NOMENCLATURE}{39}{}%
+\contentsline {section}{\hspace {-\parindent }NOMENCLATURE}{42}{}%
 \addvspace {10pt}
-\contentsline {section}{\hspace {-\parindent }BIBLIOGRAPHY}{39}{}%
+\contentsline {section}{\hspace {-\parindent }BIBLIOGRAPHY}{42}{}%
 {\hfill \ }
-\contentsline {section}{\hspace {-\parindent }APPENDIX A:\ \ {\bf \uppercase {THE FIRST APPENDIX}} }{42}{}%
+\contentsline {section}{\hspace {-\parindent }APPENDIX A:\ \ {\bf \uppercase {THE FIRST APPENDIX}} }{45}{}%
-\contentsline {section}{\hspace {-\parindent }APPENDIX B:\ \ {\bf \uppercase {THE SECOND APPENDIX}} }{43}{}%
+\contentsline {section}{\hspace {-\parindent }APPENDIX B:\ \ {\bf \uppercase {THE SECOND APPENDIX}} }{46}{}%
-\contentsline {section}{\numberline {B.1}\bf A Heading in an Appendix}{43}{}%
+\contentsline {section}{\numberline {B.1}\bf A Heading in an Appendix}{46}{}%
-\contentsline {subsection}{\numberline {B.1.1}\it A Subheading in an Appendix}{43}{}%
+\contentsline {subsection}{\numberline {B.1.1}\it A Subheading in an Appendix}{46}{}%
-\contentsline {subsubsection}{A Sub-subsection in an Appendix}{43}{}%
+\contentsline {subsubsection}{A Sub-subsection in an Appendix}{46}{}%