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 + (nlogn)/v) time and O(nv 2 + n 2) operations on the CREW PRAM, where v≤ n is a parameter. By choosing v = √n, we obtain an O(√ nlogn)-time algorithm with O(n2) operations. For v = n/logn, we have an O(log2 n)-time algorithm with O(n 3 / loit2n) operations. The previous solution takes O(log2 n) time with O(n 3 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.
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Chung, Y., Park, K., Kwon, HC. (2000). An Efficient Parallel Algorithm for Scheduling Interval Ordered Tasks. In: van Leeuwen, J., Watanabe, O., Hagiya, M., Mosses, P.D., Ito, T. (eds) Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics. TCS 2000. Lecture Notes in Computer Science, vol 1872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44929-9_9
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