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Fast Static Scheduling Algorithm for DAGs on an Unbounded Number of Processors

This presentation introduces a fast static scheduling algorithm optimized for Directed Acyclic Graphs (DAGs) on an unbounded number of processors. The algorithm, including EZ, DSC, and Clan methods, aims to minimize total processing time and reduce critical path lengths through clustering and heuristic approaches. We explore tree-structured task graphs, communication overhead, and scheduling classifications, comparing various algorithms across different test graphs to determine efficiency and speedup. The presentation highlights the advantages and complexities of Clan at varying granular levels, offering insights for broader application scenarios. References include seminal works on static scheduling algorithms for parallel processing systems.

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Fast Static Scheduling Algorithm for DAGs on an Unbounded Number of Processors

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  1. Fast Static Scheduling Algorithm for DAGs on an Unbounded Number of Processors Speaker:Si-Wen Hung Advisor:Dr. Sao-Jie Chen

  2. Outline • Introduction • Scheduling Classification • EZ • DSC • Clan • Comparison

  3. Introduction • Scheduling • Assign all the tasks to PE • Minimize the total processing

  4. Introduction • Tasks graph • Communication overhead

  5. Introduction

  6. Introduction

  7. Introduction • Tree-structured task graph

  8. Introduction • Critical path heuristic • In order to reduce the critical path by clustering • DSC • MCP • EZ

  9. Introduction • Assumptions: • Task duplication is not allowed • The number of available processors is unlimited • The task execution is triggered by the arrival of all data and at the completion of its execution the data are send in parallel to successor tasks.

  10. Algorithm.1 • Clustering steps by Sarkar’s algorithm(EZ) • Initially each task is in a separate cluster • Sort all the edges from high cost to low cost • For each edge from the sorted edge list • If set the edge to zero cost would reduce parallel time • If yes , set the two nodes of the edge to the same cluster

  11. Algorithm.1 • Example

  12. Algorithm.2 • Dominant sequence clustering algorithm (DSC) • Partial free list (PFL),Free list (FL) • Select the highest priority of node from PHL and FL • If set the node to the same cluster would reduce parallel time • If yes , set the two nodes of the edge to the same cluster • Otherwise, open new cluster for the node

  13. Algorithm.2 • Example

  14. Clan • Type • Linear • Independent • Parse Tree • Hierarchical view

  15. Clan • Parse Tree • Hierarchical view

  16. Clan • Multi-Stage Decision Graph • Find the shortest path

  17. Comparison • Granularity Analysis • 420 test graph • Speedup < 1

  18. Comparison • Normalized Relative Parallel Time • Average speed up

  19. Comparison • Efficiency of the algorithm

  20. Conclusion • Clan has high speed up ,but more complexity at low granularity • Clan is not better than other at high granularity • Clan suit the cases of wide range of granularity or low granularity

  21. References • A. Gerasoulis and T. Yang, "A Fast Static Scheduling Algorithm for DAGs on a unbounded Number of Processors," Proc. of Supercomputing'91, (Nov. 1991), pp.633-642. • T. Yang and A. Gerasoulis, "A Fast Static Scheduling Algorithm for DAGs on an Unbounded Number of Processors", Proc. Supercomputing '91, pp. 633-642 (1991). • A. A. Khan, C. L. McCreary and Y. Gong, A Numerical Comparative Analysis of Partitioning Heuristics for Scheduling Task Graphs on Multiprocessors, October 21, 1993.

  22. Another

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