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Questions and Answers
What is the most difficult step in Ian Foster's Methodology (PCAM) for parallel algorithm design?
What is the primary focus of parallel algorithm design in terms of Ian Foster's Methodology (PCAM)?
What is the term for the number of tasks that can be executed in parallel?
What is the maximum number of tasks that can be executed in parallel at any point during program execution?
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What is the graph or matrix used to illustrate partitioning?
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What determines the communication step in Ian Foster's Methodology (PCAM)?
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What happens to the degree of concurrency as the decomposition becomes finer in granularity?
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What is the term for the average number of tasks that can be processed in parallel over the execution of the program?
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What is the term for the process of breaking down a problem into smaller tasks?
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What is the term for the process of assigning tasks to processors?
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Study Notes
Preliminaries
- A directed path in the task dependency graph represents a sequence of tasks that must be processed in a specific order.
- The longest path in the graph determines the shortest time in which the program can be executed in parallel.
- The length of the longest path is called the critical path length.
Critical Path Length
- The critical path length determines the shortest parallel execution time.
- In the given graphs, the critical path lengths are 27 and 34.
Limits on Parallel Performance
- There is an inherent bound on how fine the granularity of a computation can be.
- Concurrent tasks may have to exchange data with other tasks, resulting in communication overhead.
- The tradeoff between granularity and associated overheads determines performance bounds.
Partitioning Techniques
- Recursive Decomposition: suited for problems solved using divide and conquer strategies.
- Data Decomposition
- Exploratory Decomposition
- Speculative Decomposition
Recursive Decomposition
- Decompose problems into sub-problems that can be solved in parallel.
- Need to think recursively, not sequentially.
Examples of Recursive Decomposition
- Quicksort: partitioning the list around the pivot, and processing sublists concurrently.
- Finding the Min/Max/Sum: using associative and commutative operations.
Parallel Algorithm Design
- Look at Ian Foster's Methodology (PCAM)
- Partition: decompose the problem and identify concurrent tasks.
- Communication: often dictated by partition.
- Agglomeration (clustering/blocking): often not much can be done here.
- Mapping: a difficult problem, involving load balancing.
Task Dependency Graph
- Illustrated as a directed graph or adjacency matrix.
- Nodes represent tasks, and edges denote dependencies between tasks.
Degree of Concurrency
- The number of tasks that can be executed in parallel.
- Maximum Degree of Concurrency: the maximum number of tasks at any point during execution.
- Average Degree of Concurrency: the average number of tasks processed in parallel over the execution of the program.
- The degree of concurrency increases as the decomposition becomes finer in granularity.
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Description
This quiz covers the concept of task dependency graphs in parallel computing, including the longest path and critical path length.
