Abstract
Under consideration is the NP-hard problem of makespan scheduling on two machines in the presence of a partial precedence order between the operations, with the criterion of minimization of the moment of completion of all operations. An approximation algorithm with a guaranteed precision estimate is proposed for this problem. Polynomial solvability of the problem is proved in the case when each operation on the first machine is in the precedence relation with exactly two operations on the second machine. The corresponding algorithm is developed.
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