Addresses the problem of finding near-optimal schedules for in-tree structured task graphs on a linear array with a fixed number m of identical processors. Each node of the tree requires one unit of execution time and every (directed) edge of the tree denotes that a task can begin execution only after receiving a message from all of its predecessors. The communication links between the processors are bidirectional and can transmit only one message in each direction in one unit of time. The natural goal is to prescribe a schedule that results in the fastest execution (e.g. minimizes the schedule length or makespan) of all the tasks in the tree. For this problem, we present an O(n log n) time algorithm that outputs a schedule that is guaranteed to be no more than 11 times the optimal schedule length. This is a significant improvement over the results of Kalpakis and Yesha(1993). Further, we demonstrate through simulation experiments that our algorithm performs extremely well in practice, with an approximation factor that is close to 2 and not more than 3.
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