Chapter 5 Editing
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16
Chapter5.tex
16
Chapter5.tex
@ -46,7 +46,7 @@ attack and compliance graph generation.
|
||||
\end{figure}
|
||||
|
||||
\TUsubsection{Algorithm Design}
|
||||
The design of the tasking approach is to leverage a pipeline structure with the six tasks and MPI nodes. After its completion, each stage of the pipeline will pass the necessary data to the next stage through various MPI messages, where the next stage's nodes will receive the data and execute their tasks. The pipeline is considered fully saturated when each task has a dedicated node solely for executing work for that task. When there are less nodes than tasks, some nodes will process multiple tasks. When there are more nodes than tasks, additional nodes will be assigned to Tasks 1 and 2. Timings were collected in the serial approach for various networks that displayed more time requirements for Tasks 1 and 2, with larger network sizes requiring vastly more time to be taken in Tasks 1 and 2. As a result, additional nodes are assigned to Tasks 1 and 2. Node allocation can be seen in Figure \ref{fig:node-alloc}.
|
||||
The design of the tasking approach is to leverage a pipeline structure with the six tasks and MPI nodes. After its completion, each stage of the pipeline will pass the necessary data to the next stage through various MPI messages, where the next stage's nodes will receive the data and execute their tasks. The pipeline is considered fully saturated when each task has a dedicated node solely for executing work for that task. When there are less nodes than tasks, some nodes will process multiple tasks. When there are more nodes than tasks, additional nodes will be assigned to Tasks 1 and 2. Timings were collected in the serial approach for various networks that displayed more time requirements for Tasks 1 and 2, with larger network sizes requiring vastly more time to be taken in Tasks 1 and 2. As a result, additional nodes are assigned to Tasks 1 and 2. Node allocation can be seen in Figure \ref{fig:node-alloc}. In this Figure, ``world.size()" is an integer value representing the number of nodes used in the program, and ``num_tasks" is an integer value representing the number of tasks used in the pipeline. By using a variable for the number of tasks, it allows for modular usage of the pipeline, where tasks can be added and removed without needing to change any allocation logic work; only communication between tasks may need to be modified, and the allocation can be adjusted relatively simply to include new tasks.
|
||||
|
||||
For determining which tasks should be handled by the root note, a few considerations were made, where minimizing communication cost and avoiding unnecessary complexity were the main two considerations. In the serial approach, the frontier queue was the primary data structure for the majority of the generation process. Rather than using a distributed queue or passing multiple sub-queues between nodes, the minimum cost option is to pass states individually. This approach also assists in reducing the complexity. Managing multiple frontier queues would require duplication checks, multiple nodes requesting data from and storing data into the database, and devising a strategy to maintain proper queue ordering, all of which would also increase the communication cost. As a result, the root node will be dedicated to Tasks 0 and 3.
|
||||
|
||||
@ -58,7 +58,7 @@ For determining which tasks should be handled by the root note, a few considerat
|
||||
\end{figure}
|
||||
|
||||
\TUsubsubsection{Communication Structure}
|
||||
The underlying communication structure for the tasking approach relies on a pseudo-ring structure. As seen in Figure \ref{fig:node-alloc}, nodes n$_2$, n$_3$, and n$_4$ are derived from the previous task's greatest node rank. To keep the development abstract, a custom send function checks the world size before sending. If the rank of the node that would receive a message is greater than the world size and therefore does not exist, the rank would then be ``looped around" and corrected to fit within the world size constraints. After the rank correction, the MPI Send function was then invoked with the proper node rank.
|
||||
The underlying communication structure for the tasking approach relies on a pseudo-ring structure. As seen in Figure \ref{fig:node-alloc}, nodes n$_2$, n$_3$, and n$_4$ are derived from the previous task's greatest node rank. To keep the development abstract, a custom send function checks the world size (``world.size()") before sending. If the rank of the node that would receive a message is greater than the world size and therefore does not exist, the rank would then be ``looped around" and corrected to fit within the world size constraints. After the rank correction, the MPI Send function was then invoked with the proper node rank.
|
||||
|
||||
\TUsubsubsection{Task 0}
|
||||
Task 0 is performed by the root node, and is a conditional task; it is not guaranteed to be executed at each pipeline iteration. Task 0 is only executed when the frontier is empty, but the database still holds unexplored states. This occurs when there are memory constraints, and database storage is performed during execution to offload the demand, as discussed in Section \ref{sec:db-stor}. After the completion of Task 0, the frontier has a state popped, and the root node sends the state to n$_1$. If the frontier is empty, the root node sends the finalize signal to all nodes.
|
||||
@ -136,7 +136,7 @@ A series of tests were conducted on the platform described at the beginning of S
|
||||
|
||||
The results of the Tasking Approach can be seen in Figure \ref{fig:Spd-Eff-Task}. In terms of speedup, when the number of entries in the exploit list is small, the serial approach has better performance. This is expected due to the communication cost requiring more time than it does to generate a state, as discussed in Section \ref{sec:Task-perf-expec}. 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.
|
||||
|
||||
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 any speedup on any of the testing cases conducted. Similarly, testing with 3, 4, and 5 compute nodes were relatively high compared to the ``fully saturated pipeline" testing counterparts, but they also did not provide any speedup 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.
|
||||
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.
|
||||
|
||||
\begin{figure}[htp]
|
||||
\centering
|
||||
@ -156,10 +156,10 @@ In terms of efficiency, 2 compute nodes offer the greatest value since the speed
|
||||
|
||||
\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 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.
|
||||
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.
|
||||
|
||||
\TUsubsection{Algorithm Design}
|
||||
The design of the subgraphing approach consists of three main components: worker nodes, the root node, and a database node. The original design did not include a database node, but testing through the implementation of the tasking approach discussed in \ref{sec:T4T5} led to the inclusion of a dedicated database node. The overall design is predicated on the root node distributing data to all worker nodes and merging the worker nodes' subgraphs. Figure \ref{fig:subg} displays an example graph that utilizes three worker nodes with a depth limit of 3. Each worker node corresponds to a different graph state color in the figure. Each worker node explored a varying number of states, but did not proceed to explore a depth that exceeded the specified depth limit of 3. The final cluster of four nodes at the bottom of the graph represents one of the three worker node exploring the final states, while the other two nodes wait for further instruction. The following three subsections describe each component in further detail.
|
||||
The design of the subgraphing approach consists of three main components: worker nodes, the root node, and a database node. The original design did not include a database node, but testing through the implementation of the tasking approach discussed in \ref{sec:T4T5} led to the inclusion of a dedicated database node. The overall design is predicated on the root node distributing data to all worker nodes and merging the worker nodes' subgraphs. Figure \ref{fig:subg} displays an example graph that utilizes three worker nodes with a depth limit of 3. Each worker node corresponds to a different graph state color and texture in the figure. Each worker node explored a varying number of states, but did not proceed to explore a depth that exceeded the specified depth limit of 3. The final cluster of four nodes at the bottom of the graph represents one of the three worker node exploring the final states, while the other two nodes wait for further instruction. The following three subsections describe each component in further detail.
|
||||
|
||||
\begin{figure}[htp]
|
||||
\centering
|
||||
@ -215,7 +215,7 @@ Similar to Section \ref{sec:tasking-tag} that discussed the usage of MPI Tags fo
|
||||
This approach is intended to reduce runtime when the frontier grows at a rate faster than it can be explored. However, since this approach is designed for distributed systems, there is no guarantee that speedup can be achieved when duplicate work is performed. Not only is there wasted time by the worker nodes when duplicate work occurs, but duplicate work also contributes to increased communication between nodes to adequately explore the graph, and also leads to an increased number of merging calls by the root node. The ideal scenario for the subgraphing approach is when the graph is sparse, and the graph aligns more with a N-Ary tree structure where each node only has one parent. When the graph is sparse, there is a lower likelihood of duplicate work occurring, since worker nodes have a lower probability of exploring a graph state that connects to a different graph state that has been (or will be) explored by another worker node. If each graph state was able to have only one parent, there is a lower likelihood that worker nodes would explore the same graph cluster.
|
||||
|
||||
\TUsubsection{Results} \label{sec:Subgraphing-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 Subgraphing approach on the 4 example networks discussed in \ref{sec:Sync-Test}. All tests used synchronous firing. The initial results are seen in Figure \ref{fig:Subg_base}, which displays the results in terms of their runtimes. Only the serial runtime from the 2 Service test is displayed for conciseness. The results in terms of speedup and efficiency are seen in Figure \ref{fig:Subg_SE}.
|
||||
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 Subgraphing approach on the 4 example networks discussed in \ref{sec:Sync-Test}. All tests used synchronous firing. Figure \ref{fig:Subg_base} shows the runtimes of each of the test cases. Only the serial runtime from the 2 Service test is displayed for conciseness. The results in terms of speedup and efficiency are seen in Figure \ref{fig:Subg_SE}.
|
||||
|
||||
\begin{figure}[htp]
|
||||
\includegraphics[width=\linewidth]{"./Chapter5_img/MPISubg_RT_No_DHT.png"}
|
||||
@ -232,7 +232,7 @@ A series of tests were conducted on the platform described at the beginning of S
|
||||
\label{fig:Subg_SE}
|
||||
\end{figure}
|
||||
|
||||
As noted from the Figures, the performance from this approach appears quite poor. The serial approach has greater performance in all cases, and the resulting speedups for all 4 service tests are below 1.0 when using the subgraphing approach. Likewise, the efficiency continues to worsen as more compute nodes are added to the system. There are a few reasons for this poor performance. Figure \ref{fig:subg} illustrates an example graph that is considered favorable to this approach in that branches are relatively distinct, and the graph is not fully connected. As a result in this example graph, each compute node is working on independent graph structures that do not overlap, and all work is distinct. This graph can quickly lead to issues through a few modifications. Figure \ref{fig:subg_mod} utilizes the same example graph from Figure \ref{fig:subg}, but adds two edges between the outside branches. With this arrangement, the 1st and 3rd compute nodes will perform work that overlaps with the work performed by the 2nd compute node. Both compute node 1 and compute node 3 will explore State 5, and depending on the depth limit, compute nodes 1 and 3 will continue to explore State 5's children, leading to almost all of compute 2's work being duplicated twice. This duplicate work occurs at an alarming rate in the service tests that were performed. Figure \ref{fig:subg_dup} illustrates that there is an extraordinarily large amount of duplicate work occurring in the testing, which substantially increases the runtime of this approach. The duplicate work, as discussed in Section \ref{sec:perf_expec_subg}, not only wastes compute nodes' times and leads to a longer exploration process, but it also requires the root node to perform more merging and cleanup work. When using mpiP (a light-weight MPI profiler provided by Lawrence Livermore National Laboratory) \cite{lawrence_livermore_national_laboratory_mpip_nodate}, it was measured that this extra merging and cleanup work performed by the root causes additional delays in distributing data, and the compute nodes spent a combined 35{\%} total application runtime just waiting to receive more data from the root node in the 1 service test.
|
||||
As noted from Figures \ref{fig:Subg_base} and \ref{fig:Subg_SE}, the performance from this approach appears quite poor. The serial approach has greater performance in all cases, and the resulting speedups for all 4 service tests are below 1.0 when using the subgraphing approach. Likewise, the efficiency continues to worsen as more compute nodes are added to the system. There are a few reasons for this poor performance. Figure \ref{fig:subg} illustrates an example graph that is considered favorable to this approach in that branches are relatively distinct, and the graph is not fully connected. As a result in this example graph, each compute node is working on independent graph structures that do not overlap, and all work is distinct. This graph can quickly lead to issues through a few modifications. Figure \ref{fig:subg_mod} utilizes the same example graph from Figure \ref{fig:subg}, but adds two edges between the outside branches. With this arrangement, the 1st and 3rd compute nodes will perform work that overlaps with the work performed by the 2nd compute node. Both compute node 1 and compute node 3 will explore State 5, and depending on the depth limit, compute nodes 1 and 3 will continue to explore State 5's children, leading to almost all of compute 2's work being duplicated twice. This duplicate work occurs at an alarming rate in the service tests that were performed. Figure \ref{fig:subg_dup} illustrates that there is an extraordinarily large amount of duplicate work occurring in the testing, which substantially increases the runtime of this approach. The duplicate work, as discussed in Section \ref{sec:perf_expec_subg}, not only wastes compute nodes' times and leads to a longer exploration process, but it also requires the root node to perform more merging and cleanup work. When using mpiP (a light-weight MPI profiler provided by Lawrence Livermore National Laboratory) \cite{lawrence_livermore_national_laboratory_mpip_nodate}, it was measured that this extra merging and cleanup work performed by the root causes additional delays in distributing data, and the compute nodes spent a combined 35{\%} total application runtime just waiting to receive more data from the root node in the 1 service test.
|
||||
|
||||
\begin{figure}[htp]
|
||||
\includegraphics[width=\linewidth]{"./Chapter5_img/dup.drawio.png"}
|
||||
@ -248,7 +248,7 @@ As noted from the Figures, the performance from this approach appears quite poor
|
||||
\label{fig:subg_dup}
|
||||
\end{figure}
|
||||
|
||||
To minimize the duplicate work performed, a second approach using a distributed hash table (DHT) was attempted. With a DHT, each compute node would check to ensure that they were not duplicating work. This would limit the work needed by the root node, but each worker node would need to search the DHT. Using a DHT would increase the communication overhead, but if the communication overhead was less than the time taken for duplicate work or was minimal enough to still process the frontier at a greater rate than the serial approach, then the distributed hash table would be considered advantageous. Rather than devising a unique strategy for a distributed hash table, this work made use of the Berkely Container Library (BCL), which is open-source and provides distributed data structures with easy-to-use interfaces. Since BCL is a header-only library, it allowed for minimal code alterations, and primarily just needed to be dropped into the system. Testing was repeated with an identical setup to the approach without a DHT. The results in terms of speedup and efficiency are seen in Figure \ref{fig:subg_DHT_Spd}. Results in terms of runtime between the DHT approach and the base approach are seen in Figure \ref{fig:subg_DHT_base}.
|
||||
To minimize the duplicate work performed, a second approach using a distributed hash table (DHT) was attempted. With a DHT, each compute node would check to ensure that they were not duplicating work. This would limit the work needed by the root node, but each worker node would need to search the DHT. Using a DHT would increase the communication overhead, but if the communication overhead was less than the time taken for duplicate work or was minimal enough to still process the frontier at a greater rate than the serial approach, then the distributed hash table would be considered advantageous. Rather than devising a unique strategy for a distributed hash table, this work made use of the Berkely Container Library (BCL), which is an open-source library and provides distributed data structures with easy-to-use interfaces. Since BCL is a header-only library, it allowed for minimal code alterations, and primarily just needed to be dropped into the system. Testing was repeated with an identical setup to the approach without a DHT. The results in terms of speedup and efficiency are seen in Figure \ref{fig:subg_DHT_Spd}. Results in terms of runtime between the DHT approach and the base approach are seen in Figure \ref{fig:subg_DHT_base}.
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
|
||||
14
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{\hfill \ }
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|
||||
{\hfill \ }
|
||||
|
||||
Loading…
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Reference in New Issue
Block a user