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

TL;DR

This paper introduces a new approximation algorithm with a ratio of approximately 2.542 for scheduling jobs on a single machine with precedence constraints, release dates, and weighted completion time, improving upon the long-standing previous best.

Contribution

It provides a significantly improved approximation algorithm for a classic scheduling problem, with a performance guarantee close to the Euler constant, surpassing the 1997 result.

Findings

Achieves a 2.542-approximation ratio for the problem.

First improvement since 1997 for this scheduling problem.

Algorithm performance guarantee approaches the Euler constant e.

Abstract

We present a $\sqrt{e}/(\sqrt{e}-1)$-approximation algorithm for the nonpreemptive scheduling problem to minimize the total weighted completion time of jobs on a single machine subject to release dates and precedence constraints. The previously best known approximation algorithm dates back to 1997; its performance guarantee can be made arbitrarily close to the Euler constant $e$.