# 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} }

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

#### One Citation

On the Hardness of Scheduling With Non-Uniform Communication Delays

- Computer Science
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- 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

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