Wiritng results

Data/header.txt

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Data/para_data.csv

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Data/timing.csv

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Schrick-Noah_MPI-Tasking.aux

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Schrick-Noah_MPI-Tasking.out

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Schrick-Noah_MPI-Tasking.tex

@@ -54,8 +54,7 @@ Attack Graph; Compliance Graph; MPI; High-Performance Computing; Cybersecurity;
 \section{Introduction} \label{sec:Intro}
 As the size of computer networks continues to grow, cybersecurity analysts are tasked to mitigate risk with increasing difficulty. The authors of \cite{9678822}, \cite{7993827}, and \cite{8652334} discuss how the rapidly expanding network sizes bring about drastic changes along with the requirement to shift and refocus to accommodate the expansion. This includes presenting novel architectures to support the ever-growing IPTV networks, examinations of computer viruses through epidemiology modeling, and evaluations of new routing schemes. In recent years, a greater usage of cyber-physical systems and a growing adoption of the Internet of Things (IoT) also contributes to an increased need for risk mitigation across varying types of networks, as discussed by the authors of \cite{baloyi_guidelines_2019}, \cite{allman_complying_2006}, and \cite{j_hale_compliance_nodate}. One approach for analyzing the large number of hosts and growing lists of exploits is to automate the generation of attack or compliance graphs for later use. Attack and compliance graphs are directed acyclic graphs (DAGs) that typically represent one or many systems as nodes in a graph, and any changes that could be made to them as edges. The automation of these graphs has been used and presented by authors such as \cite{ou_scalable_2006}, \cite{CPSIOT}, and \cite{ming_jo}. The graph generators will take system information and exploits to check for as input, and will exhaustively draw all possible ways that the systems may be at risk of a cybersecurity attack or at risk of violating a compliance regulation or mandate. If a system is able to be modified through a setting change (regardless of intent), have its compliance standing altered, or have a policy updated, an edge is drawn from that node to a new node with the changed system properties. This process is repeated until all possible alterations are identified and represented in the resulting attack or compliance graph.
 
-Difficulties
-Due to the expansion in network size, and with the inclusion of IoT and cyber-physical devices, the generation of attack and compliance graph quickly becomes difficult with the large number of assets needed to be processed. In addition, the number of regulatory and compliance checks, the large number of exploit and vulnerability entries available, and any custom internal standard checks or zero-day scripting causes a state space explosion in the graph generation process. As a result, these graphs become infeasible to generate and process serially.
+Due to the expansion in network size, and with the inclusion of IoT and cyber-physical devices, the generation of attack and compliance graph quickly becomes difficult with the large number of assets needed to be processed. In addition, the number of regulatory and compliance checks, the large number of exploit and vulnerability entries available, and any custom internal standard checks or zero-day scripting causes a state space explosion in the graph generation process. As a result, real-world graphs become infeasible to generate and process serially.
 
 The attack and compliance graph generation is a viable process to parallelize and deploy on High-Performance Computing (HPC) environments, and related parallel and speedup works are discussed in Section \ref{sec:rel_works}. This work presents an extension to RAGE (RAGE Attack Graph Engine \cite{cook_rage_2018}) to function on distributed computing environments to take advantage of the increased computing power using message-passing. As mentioned by the author of \cite{pacheco_introduction_2011}, MPI is a widely used message-passing API, and one goal of this work was to utilize an API that was not only familiar and accessible, but versatile and powerful for parallelizing RAGE for distributed computing platforms. This work discusses a task parallelism approach for the generation process, and uses OpenMPI for the MPI implementation.
 
@@ -302,6 +301,55 @@ All nodes are connected with a 10Gbps Infiniband interconnect.
 \subsection{Testing Process}
 Each parameter discussed in this section was individually changed until all permutations of parameters were explored. In addition to changing the parameters, all tests were conducted on a varying number of nodes. All permutations of parameters were examined on 1 compute node (serially) through 12 compute nodes. A bash script for looping through parameters was created on the distributed computing testing platform, with jobs sent to Slurm Workload Manager \cite{Slurm}. When a job is completed with Slurm, the bash script would use grep on the output file to extract the necessary data, and add it to a CSV file that was used for the data analysis.
 
+\section{Analysis and Results}
+Exploratory data analysis was performed on the resulting data using Python to ascertain data relationships. Due to the multivariate nature of the data, there is difficulty visualizing all four independent variables (parameters) and the outcome (runtime) simultaneously. Figure \ref{fig:para_coords} makes uses of Plotly's parallel coordinates to visualize the parameters and their relationship to the runtime. Using pivot tables, Figures \ref{fig:nodes-exp} and \ref{fig:appl-load} show the runtime as they relate to the average of each individual parameter. These figures display the expected outcome: as the number of nodes increase, the runtime decreases, and as the number of exploits, applicability of exploits, and database load increases, the runtime likewise increases.
+
+\begin{figure}[htp]
+    \centering
+    \includegraphics[width=\linewidth]{"./images/para_coords.png"}
+    \vspace{.2truein} \centerline{}
+        \caption{Parallel Coordinates Plot of MPI Tasking Parameters and Runtime(ms)}
+        \label{fig:para_coords}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=\linewidth]{"./images/nodes-runtime.png"}
+    \includegraphics[width=\linewidth]{"./images/exploits-runtime.png"}
+    \caption{Number of Nodes and Exploits (Averaged) vs. Runtime (ms)}
+    \label{fig:nodes-exp}
+\end{figure}
+
+\begin{figure}
+    \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)}
+    \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.
+
+\begin{figure}[htp]
+    \centering
+    \includegraphics[width=\linewidth]{"./images/overall-speedup.png"}
+    \vspace{.2truein} \centerline{}
+        \caption{Minimum, Maximum, and Mean Speedups of MPI Tasking Across All Problem Sizes}
+        \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 increase, 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 Efficiencies of MPI Tasking Across All Problem Sizes}
+        \label{fig:overall-efficiency}
+\end{figure}
+
 \section{Results} \label{sec:Tasking-Results}
 A series of tests were conducted on the platform described at the beginning of Section \ref{sec:test-platform}, and results were collected in regards to the effect of the MPI Tasking approach on increasing sizes of exploit lists for a varying number of nodes. The exploit list initially began with 6 items, and each test scaled the number of exploits by a factor of 2. The final test was with an exploit list with 49,512 entries. If all of the items in these exploit lists were applicable, the runtime would be too great for feasible testing due to the state space explosion. To prevent state-space explosion but still gather valid results, each exploit list in the tests contained 6 exploits that could be applicable, and all remaining exploits were not applicable. The not applicable exploits were created in a fashion similar to that seen in Figure \ref{fig:NA-exp}. By creating a multitude of not applicable exploits, testing can safely be conducted by ensuring state space explosion would not occur while still observing the effectiveness of the tasking approach.
 
@@ -342,7 +390,6 @@ Figures \ref{fig:Tasking-RT}, \ref{fig:Tasking-Spd}, and \ref{fig:Tasking-Eff} d
     \label{fig:Tasking-Eff}
 \end{figure}
 
-\section{Analysis}
 
 \section{Conclusion and Future Work} \label{sec:FW}