# Towards PTAS for Precedence Constrained Scheduling via Combinatorial Algorithms

@inproceedings{Li2021TowardsPF,
title={Towards PTAS for Precedence Constrained Scheduling via Combinatorial Algorithms},
author={Shi Li},
booktitle={SODA},
year={2021}
}
• Shi Li
• Published in SODA 2021
• Computer Science, Mathematics
We study the classic problem of scheduling $n$ precedence constrained unit-size jobs on $m = O(1)$ machines so as to minimize the makespan. In a recent breakthrough, Levey and Rothvoss \cite{LR16} developed a $(1+\epsilon)$-approximation for the problem with running time $\exp\Big(\exp\Big(O\big(\frac{m^2}{\epsilon^2}\log^2\log n\big)\Big)\Big)$, via the Sherali-Adams lift of the basic linear programming relaxation for the problem by $\exp\Big(O\big(\frac{m^2}{\epsilon^2}\log^2\log n\big)\Big… Expand 1 Citations #### Figures and Topics from this paper On the Hardness of Scheduling With Non-Uniform Communication Delays • Computer Science • ArXiv • 2021 The question in negative is answered by proving that there is a logarithmic hardness for the scheduling with non-uniform communication delay problem by using a surprisingly simple reduction from a problem that is called Unique Machine Precedence constraints Scheduling (UMPS). Expand #### References SHOWING 1-10 OF 17 REFERENCES Quasi-PTAS for Scheduling with Precedences using LP Hierarchies • S. Garg • Computer Science, Mathematics • ICALP • 2018 It is shown that for fixed$m$and$\epsilon$,$(\log n)^{O(1)}$rounds of Sherali-Adams hierarchy applied to a natural LP of the problem provides a$(1+\ep silon)-approximation algorithm running in quasi-polynomial time. Expand
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