The Hardness of Approximating Poset Dimension

@article{Hegde2007TheHO,
  title={The Hardness of Approximating Poset Dimension},
  author={Rajneesh Hegde and Kamal Jain},
  journal={Electronic Notes in Discrete Mathematics},
  year={2007},
  volume={29},
  pages={435-443}
}
The dimension of a partially ordered set (poset) is the minimum integer k such that the partial order can be expressed as the intersection of k total orders. We prove that there exists no polynomial-time algorithm to approximate the dimension of a poset on N elements with a factor of O(N0.5− ) for any > 0, unless NP = ZPP. The same hardness of approximation holds for the fractional version of poset dimension, which was not even known to be NP-hard. 

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