An Efficient Parallel Algorithm for Scheduling Interval Ordered Tasks

Authors:
Yoojin Chung;Kunsoo Park;Hyuk-Chul Kwon
Affiliations:
-;-;-
Venue:
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Year:
2000

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Abstract

We present an efficient parallel algorithm for scheduling n unit length tasks on m identical processors when the precedence graphs are interval orders. Our algorithm requires O(log2 v + (n log n)=v) time and O(nv2 + n2) operations on the CREW PRAM, where v ≤ n is a parameter. By choosing v = √n, we obtain an O(√n log n)-time algorithm with O(n2) operations. For v = n/log n, we have an O(log2 n)- time algorithm with O(n3/log2 n) operations. The previous solution takes O(log2 n) time with O(n3 log2 n) operations on the CREW PRAM. Our improvement is mainly due to a reduction of the m-processor scheduling problem for interval orders to that of finding a maximum matching in a convex bipartite graph.