An O(nlogn) cost parallel algorithm for the single function coarsest partition problem

  • A. Apostolico
  • C. S. Iliopoulos
  • R. Paige
Part of the Lecture Notes in Computer Science book series (LNCS, volume 269)


A CRCW PRAM algorithm is presented for computing the coarsest refinement of a partition of a finite set S of n elements with respect to a function f on S. The algorithm requires O(n) processors, O(logn) time, and and O(nlogn) space in the worst case.


Parallel Algorithm Initial Segment Tree Element Cycle Element Final Segment 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

5. References

  1. [1]
    Aho, A.V., J.E. Hopcroft and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.Google Scholar
  2. [2]
    Cole, R., Parallel merge sort, Proceedings of the 27-th IEEE Symp. on Foundations of Computer Science, Toronto, Canada, pp. 511–516 (1986).Google Scholar
  3. [3]
    Fitch, F.E., R. L. Radge and A. Wigderson, Relation between concurrent-write models of parallel computation, typescript, Div of Comp. Science, Univ. of Califomia at Berkeley, 1983.Google Scholar
  4. [4]
    Galil, Z., Optimal parallel algorithms for string matching, Proc. 16-th ACM Symp. on Theory of Computing, pp. 240–248, 1984.Google Scholar
  5. [5]
    Hopcroft, J.E., An nlogn algorithm for minimizing states in a finite automaton, in: Kohavi and Paz, ed., Theory of Machines and Computations, Academic Press, NY, pp. 189–196, 1971.Google Scholar
  6. [6]
    Iliopoulos, C.S., A logarithmic time parallel algorithm for partitioning, Purdue University, CSD-TR-603, 1986.Google Scholar
  7. [7]
    Iliopoulos, C.S., A log-time parallel algorithm for lexicographical ordering Purdue University, CSD-TR-602, 1986.Google Scholar
  8. [8]
    Kosaraju, S.R., personal communication, 1987.Google Scholar
  9. [9]
    Paige, R., R. Tarjan and R. Bonic, A linear time solution to the single function coarsest partition problem, Theoretical Computer Science 40, pp. 67–84, 1985.Google Scholar
  10. [10]
    Paige, R. and R. Tarjan, Three efficient algorithms based on partition refinement, to appear in SIAM J. Computing.Google Scholar
  11. [11]
    Shiloach, Y., Fast canonization of circular strings J. Algorithms 2, pp. 107–121, 1981.CrossRefGoogle Scholar
  12. [12]
    Tarjan, R. and U. Vishkin, An efficient parallel biconnectivity algorithm, SIAM J. Comput. 14, pp. 862–874, 1985.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • A. Apostolico
    • 1
  • C. S. Iliopoulos
    • 1
  • R. Paige
    • 2
  1. 1.Dept. of Computer SciencePurdue UniversityWest LafayetteU.S.A.
  2. 2.Dept. of Computer ScienceNew York UniversityNew York CityU.S.A.

Personalised recommendations