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Complexity Analysis of Scheduling in CAOS-Based Synthesis

  • Gaurav Singh
  • Sandeep K. Shukla
Chapter

Abstract

Scheduling, allocation and binding are three important phases of a CDFG-based synthesis process. These phases are interdependent and can be performed in different orders depending on the design flow. In some cases, two or more phases can also be performed simultaneously. Such simultaneous execution of these phases during a synthesis process will result in a solution which is globally optimal. However, the problem of performing the three phases simultaneously is NP-hard. For this reason, most CDFG-based synthesis flows perform these phases separately in order to increase the possibility of finding optimal polynomial time algorithms for each phase.

Keywords

Schedule Problem Approximation Algorithm Time Slot Peak Power Knapsack Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  1. 59.
    M. M. Halldorsson. Approximations of Weighted Independent Set and Hereditary Subset Problems. In Proceedings of the 5th Annual International Conference on Computing and Combinatorics, LNCS, pp. 261–270. Springer-Verlag, Heidelberg, Germany, 1999.Google Scholar
  2. 83.
    J. Misra. A Discipline of Multi-Programming. Springer, New York, 2001.Google Scholar
  3. 17.
    J. Blazewicz, J. K. Lenstra, and A. H. G. Rinooy Kan. Scheduling Subject to Resource Constraints: Classification and Complexity. Discrete Applied Mathematics, 5:11–24, 1983.MATHCrossRefMathSciNetGoogle Scholar
  4. 121.
    D. Zuckerman. Linear Degree Extractors and the Inapproximability of Max Clique and Chromatic Number. In Proceedings of the ACM International Symposium on Theory of Computing (STOC’00), Seattle, WA, USA, pp. 681–690, May 2006.Google Scholar
  5. 11.
    F. Baader and T. Nipkow. Term Rewriting and All That. Cambridge University Press, Cambridge, 1998.Google Scholar
  6. 118.
    D. B. West. Introduction to Graph Theory. 2nd edn. Prentice Hall, Inc., Englewood Cliffs, NJ, 2001.Google Scholar
  7. 54.
    M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, San Francisco, CA, 1979.MATHGoogle Scholar
  8. 13.
    P. Berman and T. Fujito. Approximating Independent Sets in Degree 3 Graphs. Proceedings of the 4th Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, 955:449–460, 1995.Google Scholar
  9. 25.
    S. Chaki, E. Clarke, A. Groce, J. Ouaknine, O. Strichman, and K. Yorav. Efficient Verification of Sequential and Concurrent C Programs. Formal Methods in System Design, 25(2/3): 129–166, 2004.MATHCrossRefGoogle Scholar
  10. 58.
    L. A. Hall. Approximation Algorithms for Scheduling. In: D. S. Hochbaum (ed.) Approximation Algorithms for NP-Hard Problems. PWS Publishing Company, Boston, MA, pp. 1–45, 1997.Google Scholar
  11. 107.
    G. Singh and S. K. Shukla. Low-Power Hardware Synthesis from TRS-Based Specifications. In Fourth ACM and IEEE International Conference on Formal Methods and Models for Codesign (MEMOCODE’06), Napa Valley, CA, USA, pp. 49–58, July 2006.Google Scholar
  12. 21.
    G. Campers, O. Henkes, and P. Leclerq. Graph Coloring Heuristics: A Survey, Some New Propositions and Computational Experiences on Random and Leighton’s Graphs. Proceedings of the Operational Research, 87, Buenos Aires, pp. 917–932, 1987.Google Scholar
  13. 80.
    M. Liz et al. Efficient Generation of Schedulers for Guarded Atomic Actions. Technical Memo, Bluespec Inc., 2005. http://www.bluespec.com/
  14. 51.
    U. Feige and J. Kilian. Zero Knowledge and the Chromatic Number. Journal of Computer and System Sciences, 57:187–199, 1998.MATHCrossRefMathSciNetGoogle Scholar
  15. 62.
    J. C. Hoe and A. Arvind. Hardware Synthesis from Term Rewriting Systems. In Proceeding of VLSI’99 Lisbon, Portugal, December 1999.Google Scholar
  16. 12.
    B. S. Baker. Approximation Algorithms for NP-Complete Problems on Planar Graphs. Journal of the Association for Computing Machinery, 41:153–180, 1994.MATHMathSciNetGoogle Scholar
  17. 10.
    A. Arvind, R. Nikhil, D. Rosenband, and N. Dave. High-Level Synthesis: An Essential Ingredient for Designing Complex ASICs. In Proceedings of the International Conference on Computer Aided Design (ICCAD’04), San Jose, CA, USA, pp. 775–782, November 2004.Google Scholar
  18. 61.
    A. Hertz and D. de Werra. Using Tabu Search Techniques for Graph Coloring. Computing, 39:345–351, 1987.MATHCrossRefMathSciNetGoogle Scholar
  19. 39.
    E. G. Coffman, Jr., M. R. Garey, and D. S. Johnson. Approximation Algorithms for Bin-Packing – A Survey. In: D. S. Hochbaum (ed.) Approximation Algorithms for NP-hard Problems. PWS Publishing Company, Boston, MA, pp. 46–93, 1997.Google Scholar
  20. 60.
    J. Hastad. Clique is Hard to Approximate Within n1-ε. Acta Mathematica, 182:105–142, 1999.MATHCrossRefMathSciNetGoogle Scholar
  21. 116.
    J. D. Ullman. NP-Complete Scheduling Problems. Journal of Computer and System Sciences, 10(3):384–393, June 1975.MATHCrossRefMathSciNetGoogle Scholar
  22. 66.
    H. B. Hunt, III, M. V. Marathe, V. Radhakrishnan, S. S. Ravi, D. J. Rosenkrantz, and R. E. Stearns. Parallel Approximation Schemes for a Class of Planar and Near Planar Combinatorial Problems. Information and Computation, 173(1):40–63, February 2002.MATHCrossRefMathSciNetGoogle Scholar
  23. 97.
    D. Rosenband and A. Arvind. Modular Scheduling of Guarded Atomic Actions. In Proceedings of the Design Automation Conference (DAC’04), San Diego, CA, USA, June 2004.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Intel CorporationAustinUSA
  2. 2.Bradley Department of Electrical & Computer EngineeringVirginia TechBlacksburgUSA

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