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( log 2 v+(n log n)/v) time and O( nv 2+ n 2) 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( n 2) operations. For v=n/ log n , we have an O( log 2 n) -time algorithm with O(n 3/ log 2 n) operations. The previous solution takes O( log 2 n) time with O(n 3 log 2 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.
Published Version
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