Titles for previous plots. Conclusions and Future Work

Bibliography.bib

@@ -1360,3 +1360,44 @@ month = {oct},
 keywords = {cyber-physical system, high performance computing, attack graph, breadth-first search}
 }
 
+@article{Gust,
+	author = {Gustafson, John L.},
+	title = {Reevaluating Amdahl's Law},
+	year = {1988},
+	issue_date = {May 1988},
+	publisher = {Association for Computing Machinery},
+	address = {New York, NY, USA},
+	volume = {31},
+	number = {5},
+	issn = {0001-0782},
+	url = {https://doi.org/10.1145/42411.42415},
+	doi = {10.1145/42411.42415},
+	journal = {Commun. ACM},
+	month = {may},
+	pages = {532–533},
+	numpages = {2}
+}
+
+@inproceedings{sun,
+  title={Another view on parallel speedup},
+  author={Sun, Xian-He and Ni, Lionel M},
+  booktitle={Proceedings of the 1990 ACM/IEEE conference on Supercomputing},
+  pages={324--333},
+  year={1990}
+}
+
+@inproceedings{Amdahl,
+	author = {Amdahl, Gene M.},
+	title = {Validity of the Single Processor Approach to Achieving Large Scale Computing Capabilities},
+	year = {1967},
+	isbn = {9781450378956},
+	publisher = {Association for Computing Machinery},
+	address = {New York, NY, USA},
+	url = {https://doi.org/10.1145/1465482.1465560},
+	doi = {10.1145/1465482.1465560},
+	booktitle = {Proceedings of the April 18-20, 1967, Spring Joint Computer Conference},
+	pages = {483–485},
+	numpages = {3},
+	location = {Atlantic City, New Jersey},
+	series = {AFIPS '67 (Spring)}
+	}

Schrick-Noah_MPI-Tasking.aux

@@ -112,6 +112,15 @@
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+\newlabel{fig:param-appl}{{15}{10}{Mean Speedup and Efficiency for the Applicability of Exploit Parameter Across the Number of Compute Nodes}{figure.15}{}}
+\citation{Amdahl}
+\citation{Gust}
+\citation{sun}
 \bibdata{Bibliography}
 \bibcite{9678822}{1}
 \bibcite{7993827}{2}
@@ -126,13 +135,6 @@
 \bibcite{pacheco_introduction_2011}{11}
 \bibcite{ainsworth_graph_2016}{12}
 \bibcite{yao_efficient_2018}{13}
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 \bibcite{zhang_boosting_2017}{14}
 \bibcite{dai_fpgp_2016}{15}
 \bibcite{arifuzzaman_fast_2015}{16}
@@ -145,9 +147,13 @@
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+\bibcite{li_combining_2019}{26}
+\bibcite{Slurm}{27}
+\bibcite{Amdahl}{28}
+\bibcite{Gust}{29}
+\bibcite{sun}{30}
+\bibstyle{ieeetr}
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Schrick-Noah_MPI-Tasking.bbl

@@ -140,4 +140,19 @@ M.~Li, P.~Hawrylak, and J.~Hale, ``Combining {OpenCL} and {MPI} to support
 \bibitem{Slurm}
 SchedMD, ``Slurm {Workload} {Manager}.''
 
+\bibitem{Amdahl}
+G.~M. Amdahl, ``Validity of the single processor approach to achieving large
+  scale computing capabilities,'' in {\em Proceedings of the April 18-20, 1967,
+  Spring Joint Computer Conference}, AFIPS '67 (Spring), (New York, NY, USA),
+  p.~483–485, Association for Computing Machinery, 1967.
+
+\bibitem{Gust}
+J.~L. Gustafson, ``Reevaluating amdahl's law,'' {\em Commun. ACM}, vol.~31,
+  p.~532–533, may 1988.
+
+\bibitem{sun}
+X.-H. Sun and L.~M. Ni, ``Another view on parallel speedup,'' in {\em
+  Proceedings of the 1990 ACM/IEEE conference on Supercomputing}, pp.~324--333,
+  1990.
+
 \end{thebibliography}

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Schrick-Noah_MPI-Tasking.tex

@@ -378,6 +378,13 @@ Speedups and efficiencies were also computed across each parameter. Using pivot
 
 
 \section{Conclusion and Future Work} \label{sec:FW}
+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.
+
+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.
+
+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.
+
+The analysis portion of this work also has room for additional investigations. This work measured speedup according to Amdahl \cite{Amdahl}. Since tasks are clearly defined and timing data is collected for each task, other speedup metrics can be used. Both Gustafson's Law \cite{Gust} and Sun and Ni's Law \cite{sun} can be leveraged to obtain other results regarding the speedup of the tasking approach.
 
 %\bibliographyp
 \bibliography{Bibliography}