Constraining results to preliminary results only
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\bibcite{li_combining_2019}{26}
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\bibcite{Amdahl}{28}
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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.
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\section{Analysis and Results}
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Due to a limited amount of compute time, only preliminary results were gathered, instead of deploying the entire testing benchmark suite. The preliminary results gathered were intended to be the ``slowest" tests that would have the lowest speedup. The ``worst-case", minimum-bound data was collected to determine potential success of this approach. If the slowest tests still yielded promising speedups or efficiencies, then this approach would be viable and appealing for future, in-depth testing that could stress each component of the generation process.
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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.
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\begin{figure}[htp]
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\label{fig:overall-efficiency}
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\end{figure}
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Speedups and efficiencies were also computed across each parameter. Using pivot tables, mean speedups and mean efficiencies were computed for a parameter across all node configurations. Figures \ref{fig:param-exploit}, \ref{fig:param-appl}, \ref{fig:param-load} display the speedups and efficiencies of the exploit parameter, applicability of exploits parameter, and the database load parameter, respectively. The number of nodes has the largest impact on the exploit parameter, and Figure \ref{fig:param-exploit} illustrates that even when fewer nodes are used, speedup can still be obtained as the exploit list grows in size. Figure \ref{fig:param-appl} demonstrates that though Task 2 has less of an impact on overall runtime and contribution to speedup, speedup is still achievable as more compute nodes are added and as the applicability of exploits increase. Figure \ref{fig:param-load} highlights the increasing runtime as more database operations are performed. By dedicating nodes to solely handle database operations, the tasking pipeline is able to move to new state generation without the need to wait for all preceding database operations to complete.
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Speedups and efficiencies were also computed across each parameter. Using pivot tables, mean speedups and mean efficiencies were computed for a parameter across all node configurations. Figures \ref{fig:param-exploit}, \ref{fig:param-appl}, \ref{fig:param-load} display the speedups and efficiencies of the exploit parameter, applicability of exploits parameter, and the database load parameter, respectively. The number of nodes has the largest impact on the exploit parameter, and Figure \ref{fig:param-exploit} illustrates that even when fewer nodes are used, speedup can still be obtained as the exploit list grows in size. Figure \ref{fig:param-appl} demonstrates that though Task 2 has less of an impact on overall runtime and contribution to speedup, speedup is still achievable as more compute nodes are added and as the applicability of exploits increase. Though database load was not a parameter to easily include in preliminary testing, speedup is expected as this parameter changes. By dedicating nodes to solely handle database operations, the tasking pipeline is able to move to new state generation without the need to wait for all preceding database operations to complete.
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\begin{figure}
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\centering
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\label{fig:param-appl}
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\caption{Mean Speedup and Efficiency for the Database Load Parameter Across the Number of Compute Nodes}
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\label{fig:param-load}
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\end{figure}
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\section{Conclusion and Future Work} \label{sec:FW}
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This work presents a task parallelism approach for large-scale attack and compliance graphs. This approach is a distributed approach rather than a shared-memory approach, allowing for the generation of these large-scale graphs to be deployed on HPC systems. Tasks were identified in the generation process, with parallelization of the tasks clearly identified and incorporated into the tasking algorithm. The results of this approach highlighted its success, showing speedups as generation parameters and the number of nodes increased. Efficiencies were also computed, with various figures illustrating the efficiency across the generation process as a whole, as well as efficiencies across individual parameters.
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Though the results presented in this work were preliminary, they still highlight the viability of this approach. Despite each Task having limited stress during the generation process, speedups of over 3.5x can still be obtained. Exploit applicability and database load parameters were almost entirely unexplored during the preliminary result benchmarking, and speedup is still achievable. As exploit applicability and database load are introduced into the generation process, both speedup and efficiency are expected to increase in future testing. With more compute time, the approach of this work can be deployed on a testing platform to examine how speedups and efficiencies change as the complexity of the generation process increases.
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Future work can be performed to investigate and improve the method of this work. This work focused on a distributed approach to large-scale graph generation, but leaves room for additional parallelism at the node-level. For example, after work for Tasks 1 or 2 has been distributed to a node, the node can then leverage OpenMP for additional parallelism. Results can be obtained to show how the additional parallelism affects the speedup and efficiency of the approach.
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Additional work can be performed to investigate long-term speedup and efficiency of the approach. This work made use of a local HPC cluster with a limited number of compute nodes. The generation algorithm can be deployed to larger clusters to measure speedup and efficiency as more nodes are added to the tasking pipeline. Scalability can likewise be reexamined as the number of nodes increases.
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