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CISC 372 5 October

CISC 372 5 October. Goals for today: Foster’s parallel algorithm design Partitioning Task dependency graph Granularity Concurrency Collective communication. Task. Channel. Task/Channel Model. Parallel Algorithm Design. Large problem May be complex May have large data set

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CISC 372 5 October

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  1. CISC 372 5 October Goals for today: • Foster’s parallel algorithm design • Partitioning • Task dependency graph • Granularity • Concurrency • Collective communication

  2. Task Channel Task/Channel Model

  3. Parallel Algorithm Design • Large problem • May be complex • May have large data set • May be “embarrassingly parallel” • How “solve” problem? (Foster’s Methodology) • Partition problem & data • Determine communication requirements • Agglomerate tasks into more efficient size • Map tasks to processors

  4. Foster’s Methodology

  5. Partitioning • Dividing computation and data into pieces • Domain decomposition • Divide data into pieces • Determine how to associate computations with the data • Functional decomposition • Divide computation into pieces • Determine how to associate data with the computations

  6. Partitioning Checklist • At least 10x more primitive tasks than processors in target computer • Minimize redundant computations and redundant data storage • Primitive tasks roughly the same size • Number of tasks an increasing function of problem size

  7. Foster’s Methodology

  8. Communication • Determine values passed among tasks • Local communication • Task needs values from a small number of other tasks • Create channels illustrating data flow • Global communication • Significant number of tasks contribute data to perform a computation • Don’t create channels for them early in design

  9. Communication Checklist • Communication operations balanced among tasks • Each task communicates with only small group of neighbors • Tasks can perform communications concurrently • Task can perform computations concurrently

  10. Foster’s Methodology

  11. Agglomeration • Grouping tasks into larger tasks • Goals • Improve performance • Maintain scalability of program • Simplify programming • In MPI programming, goal often to create one agglomerated task per processor

  12. Agglomeration to Improve Performance • Eliminate communication between primitive tasks agglomerated into consolidated task • Combine groups of sending and receiving tasks

  13. Agglomeration Checklist • Locality of parallel algorithm has increased • Replicated computations take less time than communications they replace • Data replication doesn’t affect scalability • Agglomerated tasks have similar computational and communications costs • Number of tasks increases with problem size • Number of tasks suitable for likely target systems • Tradeoff between agglomeration and code modifications costs is reasonable

  14. Foster’s Methodology

  15. Mapping • Process of assigning tasks to processors • Centralized multiprocessor: mapping done by operating system • Distributed memory system: mapping done by user • Conflicting goals of mapping • Maximize processor utilization • Minimize interprocessor communication

  16. Mapping Example

  17. Optimal Mapping • Finding optimal mapping is NP-hard • Must rely on heuristics

  18. Mapping Checklist • Considered designs based on one task per processor and multiple tasks per processor • Evaluated static and dynamic task allocation • If dynamic task allocation chosen, task allocator is not a bottleneck to performance • If static task allocation chosen, ratio of tasks to processors is at least 10:1

  19. Complex Mesh Decomposition Mesh Cube With Hollow Sphere inside Cross-section of Cube • Finite number of tetrahedra • Each tetrahedron varies in size

  20. Tetra-he-who? • Tetrahedron: A solid having four triangular faces Maybe not this. This is a tetrahedron.

  21. Static Task Number,Unstructured Comm, Mesh Cube Partitioned with METIS

  22. Edge Detection • Finite number of pixels • All pixels same size • All pixel values constrained (0-255) • Stencil computation

  23. Electromagnetic Fields • Finite number of points • Laplacian equation (Jacobi method - iterate until converge on solution) • Convergence time varies at each point • Rough surface sphere • Radiation source at center • Measure strength on surface

  24. Parallel Tree Search • Unbalanced tree • Nodes may change from active to inactive at any time • Searching for specific object in set of all active nodes

  25. Online Sort • Receive list in separate pieces at different times (constant update) • Keep list sorted at all times

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