31 Questions
What is the most challenging step in Ian Foster's methodology for parallel algorithm design?
Partition
What is the main purpose of partitioning in parallel algorithm design?
To decompose the problem into concurrent tasks
What is a task dependency graph?
A directed graph illustrating task dependencies
What is the degree of concurrency?
The average number of tasks that can be executed in parallel
How does the granularity of decomposition affect the degree of concurrency?
Finer granularity increases degree of concurrency
What is the maximum degree of concurrency?
The maximum number of tasks that can be executed in parallel at any point
What is the purpose of agglomeration in parallel algorithm design?
To group tasks into clusters
What is the primary focus of parallel algorithm design?
Partitioning and Mapping
What is the purpose of mapping in parallel algorithm design?
To allocate tasks to processing units
What is the main challenge in mapping tasks to processing units?
Load balancing
What is the key strategy for solving problems using Recursive Decomposition?
Divide and Conquer
Which of the following is a characteristic of Recursive Decomposition?
Often results in natural concurrency
What is the key benefit of Recursive Decomposition in Quicksort?
Enables parallel processing of sublists
What type of operation can be used in Recursive Decomposition for finding Min/Max/Sum?
Any associative and commutative operation
What is the key mindset required for Recursive Decomposition?
Parallel thinking
What is the primary benefit of using Recursive Decomposition?
Enables parallel processing of sub-problems
Which of the following is NOT a partitioning technique?
Divide and Conquer
What is the purpose of Recursive Decomposition in problem-solving?
To enable parallel processing of sub-problems
Which of the following is a characteristic of Quicksort?
Uses recursive decomposition
What is the key difference between Recursive Decomposition and other partitioning techniques?
It often results in natural concurrency
What is the key advantage of using Recursive Decomposition compared to other techniques?
It enables parallel processing of sub-problems
What does a directed path in the task dependency graph represent?
A sequence of tasks that must be processed one after the other
What determines the shortest time in which a program can be executed in parallel?
The length of the longest path in the task dependency graph
What is the critical path length?
The length of the longest path in the task dependency graph
If each task takes 10 time units, what is the minimum parallel execution time for the graph in (a)?
34 time units
Why can't the parallel time be made arbitrarily small by making the decomposition finer in granularity?
Because of the tradeoff between granularity and overhead
What is a limitation of decomposing a computation into finer granularity?
It increases the communication overhead
What is an example of a computation that has a limit on how fine the granularity can be?
Matrix multiplication with a vector
What is the tradeoff that determines performance bounds?
Between granularity and overhead
What is the effect of communication overhead on parallel performance?
It increases the parallel execution time
What is the relationship between the critical path length and the parallel execution time?
The critical path length is equal to the parallel execution time
Study Notes
Parallel Algorithm Design
- Ian Foster's Methodology (PCAM) for parallel algorithm design involves four steps: Partition, Communication, Agglomeration, and Mapping.
- Partition: decompose the problem, identify concurrent tasks, and identify dependencies between tasks.
- Communication: often dictated by partitioning, and involves exchange of data between tasks.
- Agglomeration (clustering/blocking): grouping tasks together, but often there's limited flexibility in this step.
- Mapping: assigning tasks to processors, a difficult problem that involves load balancing.
Preliminaries
- Task Dependency Graph: a directed graph representing 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 that can be executed in parallel at any point during execution.
- Average Degree of Concurrency: the average number of tasks that can be processed in parallel over the execution of the program.
Task Dependency Graph
- A sequence of tasks that must be processed one after the other is represented by a directed path in the task dependency graph.
- 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.
Limits on Parallel Performance
- There is an inherent bound on how fine the granularity of a computation can be.
- Excessive decomposition can lead to communication overhead and diminishing returns.
- The tradeoff between granularity and overhead determines performance bounds.
Partitioning Techniques
- There is no single recipe that works for all problems.
- Common techniques include:
- Recursive Decomposition: suited to problems solved using a divide-and-conquer strategy.
- Data Decomposition: dividing the data into smaller pieces and processing each piece concurrently.
- Exploratory Decomposition: exploring different decomposition strategies to find the best one.
- Speculative Decomposition: decomposing the problem into smaller tasks and solving them concurrently, without knowing which one will be successful.
Recursive Decomposition
- Suited to problems solved using a divide-and-conquer strategy.
- Decompose based on sub-problems, which can be solved in parallel.
- Need to think recursively, not sequentially.
Examples
- Quicksort: a problem that can be solved using recursive decomposition.
- Finding the Min/Max/Sum: an example of an associative and commutative operation that can be parallelized using recursive decomposition.
Explore Ian Foster's methodology for parallel algorithm design, focusing on partitioning and mapping. Learn how to decompose problems and identify concurrent tasks.
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