An efficient parallel algorithm for scheduling interval ordered tasks

Authors:
Yoojin Chung;Kunsoo Park
Affiliations:
Department of Computer Engineering, Hankuk University of Foreign Studies, Kyonggi-do 449-791, South Korea;School of Computer Science and Engineering, Seoul National University, Seoul 151-742, South Korea
Venue:
Journal of Complexity
Year:
2003

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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 can be any number between 1 and n. 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 simple dynamic programming recurrence for computing the lengths of optimal schedules and a reduction of the m-processor scheduling problem for interval orders to that of finding a maximum matching in a convex bipartite graph.