Three, four, five, six, or the complexity of scheduling with communication delays

@article{Hoogeveen1994ThreeFF,
  title={Three, four, five, six, or the complexity of scheduling with communication delays},
  author={Han Hoogeveen and Jan Karel Lenstra and Bart Veltman},
  journal={Oper. Res. Lett.},
  year={1994},
  volume={16},
  pages={129-137}
}
A set of unit·time tasks has to be processed on identical parallel processors subject to precedence constraints and unit·time communication delays; does there exist aschedule of length at most d? The problem has two variants, depending on whether the number of processors is res· trictively small or not. For the first variant the question can be answered in polynomial time for d =3 and is NP-complete for d =4. The second variant is solvable in polynomial time for d =5 and Np. complete for d=6… CONTINUE READING
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