Scheduling algorithms for a chain-like task system

  • Chan Chi-Lok 
  • Gilbert Young 
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 762)


The optimal allocation of a chain-like task system on the chain-like network computers was first presented by Bokhari with time complexity O(m3n)[1], where m and n denote the number of modules and the number of processors respectively. Sheu and Chiang improved it and gave an O(min{{m,n}{itm2) algorithm[2]. Hsu had further developed a two phase approach with the worst case time complexity of O(m+ (m′−n)2n)[3] where m′ denotes the number of the remaining modules after the merge phase. For all of these papers, none of them answers the decision version of this problem, that is whether there exists a schedule with schedule length less than a given deadline. In this paper, two algorithms are presented. The first one answers the decision problem and gives a feasible schedule if there exists one. It is an optimal algorithm with time complexity of O(m). The second one finds an optimal schedule in O(m+ m′ log m′ + m′2n2) time using the first algorithm. It is shown that our approach is more efficient than Hsu's one if m′−n=Ω(√log n).


bottleneck processor chain-like task system completion time contiguity constraint feasible length-κ schedule layered graph merged module optimal schedule schedule length un-mergeable modules 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Shahid H. Bokhari. Partitioning problems in parallel, pipelined, and distributed computing. IEEE Transactions on Computers, 37:48–57, January 1988.CrossRefGoogle Scholar
  2. 2.
    J.P, Sheu and Z.F. Chaing. Efficient allocation of chain-like task on chain-like network computers. Information Processing Letters, 36:241–245, 1990.MathSciNetGoogle Scholar
  3. 3.
    C.C. Hsu. A two-phase approach for the optimal assignment of a chain-like task on a chain-like network computer. Technical report, National Taiwan Institute of Technology, 1993.Google Scholar
  4. 4.
    Manuel Blum, Robert W. Floyd, Vaughan Pratt, Rivest Ronald L., and Robert E. Tarjan. Time bounds for selection. Journal of Computer and System Science, 7(4):448–461, 1973.Google Scholar
  5. 5.
    C.A.R. Hoare. Algorithm 63(partition) and algorithm 65(find). Communication of ACM, 4(7):321–322, 1961.CrossRefGoogle Scholar
  6. 6.
    Robert W. Floyd and Ronald L. Rivest. Expected time bounds of selection. Communication of ACM, 18(3):165–172, 1975.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Chan Chi-Lok 
    • 1
  • Gilbert Young 
    • 1
  1. 1.The Chinese University of Hong KongHong Kong

Personalised recommendations