An Efficient Parallel Algorithm for Scheduling Interval Ordered Tasks

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 v + (n logn)/v) time and O(nv + n) operations on the CREW PRAM, where v ≤ n is a parameter. By choosing v = √ n, we obtain an O( √ n logn)-time algorithm with O(n) operations. For v = n/ logn, we have an O(log n)time algorithm with O(n/ log n) operations. The previous solution takes O(log n) time with O(n log 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.