Parallel sorting

@article{Bollobs1983ParallelS,
  title={Parallel sorting},
  author={B{\'e}la Bollob{\'a}s and Andrew Thomason},
  journal={Discrete Applied Mathematics},
  year={1983},
  volume={6},
  pages={1-11}
}
We show that if n is sufficiently large then there is a graph G of order n with In”’ log n] edges such that the transitive closure of every acyclic orientation of G has at least (,“) n3” log n edges. A consequence of this is that with Ln3’* log n] parallel processors n objects may be sorted in two time intervals. This improves considerably some results of Haggkvist and Hell. We prove similar assertions about sorting with only d-step implications. 

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