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Towards Understanding the Effective Parallelization of Sequential Algorithms

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Computer Science
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Abstract

There are very few parallel programming paradigms that consistently produce fast parallel algorithms. Divide-and-conquer is the one notable exception. The most common approach to parallel algorithm development is to try and parallelize existing sequential algorithms. The goal of this paper is to further our understanding about why some sequential algorithms parallelize better than others. We study the maximum acyclic subgraph problem and several closely related sequential approximation algorithms for it. The standard parallelization approach is applied to the sequential algorithms and vastly different parallel complexities are obtained for the resultant algorithms. That is, some of our parallel algorithms run in NC, whereas decisions problems based on others turn but to be P-complete. We find the contrasting nature of these results interesting.

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References

  1. B. Berger. The fourth moment method. In Proceedings of the Second Annual ACM-SIAM Symposium on Discrete Algorithms, pages 373–383. Association for Computing Machinery, 1991.

    Google Scholar 

  2. B. Berger and P. Shor. Approximation algorithms for the maximum acyclic subgraph problem. In Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 236–243. Association for Computing Machinery, 1990.

    Google Scholar 

  3. D.P. Bovet, S. De Agostino, and R. Petreschi. Parallelism and the feedback vertex set problem. Information Processing Letters, 28(2):81–85, June 1988.

    Article  MathSciNet  MATH  Google Scholar 

  4. S.A. Cook. A taxomy of problems with fast parallel algorithms. Information and Control 641-32–22 1985

    Google Scholar 

  5. M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. H. Freeman, San Francisco, 1978.

    Google Scholar 

  6. L. M. Goldschlager, R. A. Shaw, and J. Staples. The maximum flow problem is log space complete for P. Theoretical Computer Science, 21:105–111, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Greenlaw. Ordered vertex removal and subgraph problems. Journal of Computer and System Sciences, 39(3):323–342, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Greenlaw. The parallel complexity of approximation algorithms for the maximum acyclic subgraph problem. Technical Report 91-13, University of New Hampshire, 1991.

    Google Scholar 

  9. R. Greenlaw. A model classifying algorithms as inherently sequential with applications to graph searching. Information and Computation, to appear.

    Google Scholar 

  10. R. Greenlaw, H.J. Hoover, and W.L. Ruzzo. A compendium of problems complete for P: Parts I and II. Technical Report 91-11, University of Alberta, and Technical Report 91-05-01, University of Washington, to appea

    Google Scholar 

  11. R.M. Karp. Reducibility Among Combinatorial Problems, pages 85–103. Plenum Press, New York, 1972.

    Google Scholar 

  12. R.M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In Handbook of Theoretical Computer Science. MIT Press, 1990.

    Google Scholar 

  13. S. Miyano. The lexicographically first maximal subgraph problems: P-completeness and NC algorithms. Mathematical Systems Theory, 22(1):47–73, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  14. V. Ramachandran. The complexity of minimum cut and maximum flow problems in an acyclic network. Networks, 17:387–392, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  15. V. Ramachandran. Fast and processor-efficient parallel algorithms for reducible flow graphs. Technical Report UILU-ENG-88-2257, ACT-103, University of Illinois at Urbana-Champaign, November 1988.

    Google Scholar 

  16. V. Ramachandran. Finding a minimum feedback arc set in reducible flow graphs. Journal of Algorithms, 9(3):299–313, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. Shamir. A linear time algorithm for finding minimum cutsets in reducible graphs. SIAM Journal of Computing, 8(4):645–655, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  18. C.C. Wang, E.L. Llyod, and M.L. Soffa. Feedback vertex sets and cyclically reducible graphs. Journal of the ACM, 32(2):296–313, April 1985.

    Article  MATH  Google Scholar 

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© 1992 Springer Science+Business Media New York

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Greenlaw, R. (1992). Towards Understanding the Effective Parallelization of Sequential Algorithms. In: Baeza-Yates, R., Manber, U. (eds) Computer Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3422-8_33

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  • DOI: https://doi.org/10.1007/978-1-4615-3422-8_33

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6513-6

  • Online ISBN: 978-1-4615-3422-8

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