An Almost-Optimal Algorithm for the Assembly Line Scheduling Problem

This paper considers a solution to the multiprocessor scheduling problem for the case where the ordering relation between tasks can be represented as a tree. Assume that we have n identical processors, and a number of tasks to perform. Each task T
i
requires an amount of time μ
i
to complete, 0 < μ
i
≤ k, so that k is an upper bound on task time. Tasks are indivisible, so that a processor once assigned must remain assigned until the task completes (no preemption). Then the "longest path" scheduling method is almost-optimal in the following sense.