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arXiv · 2309.12031

Simple Approximation Algorithms for Minimizing the Total Weighted Completion Time of Precedence-Constrained Jobs

Sven Jäger·Philipp Warode
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Abstract

We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show that the same ratio is achieved by a simple weighted round-robin rule. Moreover, for preemptive scheduling on identical parallel machines, we give a strongly polynomial $3$-approximation, which computes processing rates by solving a sequence of parametric flow problems. This matches the best known constant performance guarantee, previously attained only by a weakly polynomial LP-based algorithm. Our algorithms are both also applicable in non-clairvoyant scheduling, where processing times are initially unknown. In this setting, our performance guarantees improve upon the best competitive ratio of $8$ known so far.

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Sven Jäger, Philipp Warode. 2023-09-21. Simple Approximation Algorithms for Minimizing the Total Weighted Completion Time of Precedence-Constrained Jobs. https://arxiv.org/abs/2309.12031

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