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CS 584 Lecture 3

CS 584 Lecture 3. How is the assignment going?. Designing Parallel Algorithms. Designing a parallel algorithm is not easy. There is no recipe or magical ingredient Except creativity We can benefit from a methodical approach. Framework for algorithm design

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CS 584 Lecture 3

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  1. CS 584 Lecture 3 • How is the assignment going?

  2. Designing Parallel Algorithms • Designing a parallel algorithm is not easy. • There is no recipe or magical ingredient • Except creativity • We can benefit from a methodical approach. • Framework for algorithm design • Most problems have several parallel solutions which may be totally different from the best sequential algorithm.

  3. PCAM Algorithm Design • 4 Stages to designing a parallel algorithm • Partitioning • Communication • Agglomeration • Mapping • P & C focus on concurrency and scalability. • A & M focus on locality and performance.

  4. PCAM Algorithm Design • Partitioning • Computation and data are decomposed. • Communication • Coordinate task execution • Agglomeration • Combining of tasks for performance • Mapping • Assignment of tasks to processors

  5. Partitioning • Ignore the number of processors and the target architecture. • Expose opportunities for parallelism. • Divide up both the computation and data • Can take two approaches • domain decomposition • functional decomposition

  6. Domain Decomposition • Start algorithm design by analyzing the data • Divide the data into small pieces • Approximately equal in size • Then partition the computation by associating it with the data. • Communication issues may arise as one task needs the data from another task.

  7. 1 4 ò + 2 1 x 0 Domain Decomposition • Evaluate the definite integral. 0 1

  8. Split up the domain 0 1

  9. Split up the domain 0 1

  10. Split up the domain Now each task simply evaluates the integral in their range. All that is left is to sum up each task's answer for the total. 0 0.25 0.5 0.75 1

  11. Domain Decomposition • Consider dividing up a 3-D grid • What issues arise? • Other issues? • What if your problem has more than one data structure? • Different problem phases? • Replication?

  12. Functional Decomposition • Focus on the computation • Divide the computation into disjoint tasks • Avoid data dependency among tasks • After dividing the computation, examine the data requirements of each task.

  13. Functional Decomposition • Not as natural as domain decomposition • Consider search problems • Often functional decomposition is very useful at a higher level. • Climate modeling • Ocean simulation • Hydrology • Atmosphere, etc.

  14. Partitioning Checklist • Define a LOT of tasks? • Avoid redundant computation and storage? • Are tasks approximately equal? • Does the number of tasks scale with the problem size? • Have you identified several alternative partitioning schemes?

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