Scheduling interval ordered tasks in parallel

  • S. Sunder
  • Xin He
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


We present the first NC algorithm for scheduling n unit length tasks on m identical processors for the case where the precedence constraint is an interval order. Our algorithm runs on a priority CRCW PRAM in O(log2n) time with O(n5) processors, or in O(log3n) time with O(n4) processors. The algorithm constructs the same schedule as the one produced by the sequential algorithm (list scheduling). On the other hand, we show that when the precedence constraints are allowed to be arbitrary, the construction of the list schedule is P-complete.


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  1. 1.
    J. D. Ullman. Complexity of sequencing problems. In E. G. Coffman, editor, Computer and Job Scheduling Theory. John Wiley and sons, 1976.Google Scholar
  2. 2.
    E. G. Coffman and R. L. Graham. Optimal scheduling for two processor systems. Acta Informatica, 1:200–213, 1971.Google Scholar
  3. 3.
    M. R. Garey and D. S. Johnson. Scheduling tasks with nonuniform deadlines on two processors. Journal of the ACM, 23:461–467, 1976.Google Scholar
  4. 4.
    H. N. Gabow. An almost linear time algorithm for two processor scheduling. J. Assoc. Comput. Mach., 29:766–780, 1982.Google Scholar
  5. 5.
    M. Bartusch, R. H. Mohring, and F. J. Radermacher. M-machine unit time scheduling: a report of ongoing research, volume 304 of Lecture Notes in Economics and Mathematical Systems, pages 165–212. Springer-Berlin, 1988.Google Scholar
  6. 6.
    T. C. Hu. Parallel sequencing and assembly line problems. Operations Research, 9:841–848, 1961.Google Scholar
  7. 7.
    C. H. Papadimitriou and M. Yannakakis. Scheduling interval-ordered tasks. SIAM J. on Computing, 8:405–409, 1979.Google Scholar
  8. 8.
    E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys. Sequencing and scheduling: Algorithms and complexity. Technical report, Centrum voor Wiskunde en Informatica, 1989.Google Scholar
  9. 9.
    D. Helmbold and E. Mayr. Fast Scheduling Algorithms on Parallel Computers. Advances in Computing Research. Jai press inc., London, 1987.Google Scholar
  10. 10.
    D. HelmBold and E. Mayr. Two processor scheduling is in NC. SIAM J. on Computing, 16:747–759, August 1987.Google Scholar
  11. 11.
    H. Jung, P. Spirakis, and M. Serna. A parallel algorithm for two processors precedence constrained scheduling. In Proceedings of ICALP, 1991.Google Scholar
  12. 12.
    D. Dolev, E. Upfal, and M. Warmuth. Scheduling trees in parallel. In P. Bertolazzi and F. Luccio, editors, VLSI: Algorithms and Architectures, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • S. Sunder
    • 1
  • Xin He
    • 1
  1. 1.Department of Computer ScienceState University of New York at BuffaloBuffaloUSA

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