ISAAC 1994: Algorithms and Computation pp 607-615

# Efficient algorithms for assigning chain-like tasks on a chain-like network computer

• Gilbert H. Young
• Chi-Lok Chan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 834)

## Abstract

The optimal allocation of a chain-like task system on a chain like network computers has been studied in a number of papers [1][2][3][4]. The best known algorithm has a time complexity of O((m′-n)2n) if m′n=O(√log n); otherwise O(m′ log m′ + m′(m′-n)) where m′ and n denote the number of un-mergeable modules and the number of processors respectively[4]. The space complexity of Hsu's algorithm and Young and Chan's algorithm are ((m′−n)n) and O(m′(m′−n)) respectively. In this paper, we generalize the decision algorithm discussed in [4] and propose two algorithms for the optimization problem based on the generalized decision test. The first algorithm gives an optimal schedule in O(m′2) time. For the second one, the chain-like task system is divided into two categories, dominated and non-dominated task system. A dominated task system can be solved by an asymptotically optimal algorithm in O(m′) time. For a non-dominated task system, the worst case time complexity is O(m′n log(m′n)). This is asymptotically the best algorithm if m′n=ω(n). This algorithm has an efficient average case time complexity of O(m′ log m′) which is better than all existing algorithms except m′−n=o(√log n). The space complexity of our algorithm is O(m′) which is better than that of Young and Chan's or Hsu's algorithm. Furthermore, the optimal schedules obtained by using all these algorithms share a common property that the minimal number of processors is always used so that they are the optimally load balanced optimal schedules.

## References

1. 1.
Shahid H. Bokhari. “Partitioning Problems in Parallel, Pipelined, and Distributed Computing”. IEEE Transactions on Computers, vol 37:pp. 48–57, January 1988.Google Scholar
2. 2.
J.P. Sheu and Z.F. Chaing. “Efficient allocation of chain-like task on chain-like network computers”. Information Processing Letters, vol 36:pp. 241–245, 1990.
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.
Gilbert Young and Chan Chi-Lok. “Scheduling Algorithm for a Chain-like Task System”. In “Lecture Notes in Computer Science”, volume vol: 762, pages 496–515, 1993.Google Scholar