Scheduling Algorithms for a Chain-like Task System

The optimal allocation of a chain-like task system on the chain-like network computers was rst presented by Bokhari with time complexity O(m 3 n))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(minfm; ngm 2) algorithmm2]. Hsu had further developed a two phase approach with the worst case time complexity of O(m+(m 0 ?n) 2 n))3] where m 0 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 rst 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 nds an optimal schedule in O(m+m 0 log m 0 +m 02 ?n 2) time using the rst algorithm. It is shown that our approach is more eecient than Hsu's one if m 0 ?n = !(p log n). Furthermore, our algorithm returns an optimal schedule which uses the minimal number of processors.