Towards PTAS for Precedence Constrained Scheduling via Combinatorial Algorithms

  title={Towards PTAS for Precedence Constrained Scheduling via Combinatorial Algorithms},
  author={Shi Li},
  • 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
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