Abstract
We consider the problem of scheduling a set of tasks whose precedence relation is representable as a directed forest, on two identical machines, in order to minimize the total completion time. A new heuristic algorithm is presented which provides a 1 4 approximate solution. This algorithm is based on the idea of critical jobs, where a job is a set of tasks corresponding to a maximal tree in the forest. A critical job is one whose total duration exceeds the total duration of all other jobs. In the paper, first a 1 4 approximate algorithm for the case in which no job is critical is presented, then this algorithm is extended to the general case. The 1 4 approximate bound is proved to be tight. The complexity of the proposed algorithm is studied.
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