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We present a $\sqrt{e}/(\sqrt{e}-1)$-approximation algorithm for thenonpreemptive scheduling problem to minimize the total weighted completion timeof jobs on a single machine subject to release dates and precedenceconstraints. The previously best known approximation algorithm dates back to1997; its performance guarantee can be made arbitrarily close to the Eulerconstant $e$.

A 2.542-Approximation for Precedence Constrained Single Machine Scheduling with Release Dates and Total Weighted Completion Time Objective