Polylogarithmic inapproximability

@inproceedings{Halperin2003PolylogarithmicI,
  title={Polylogarithmic inapproximability},
  author={Eran Halperin and Robert Krauthgamer},
  booktitle={STOC '03},
  year={2003}
}
We provide the first hardness result of a polylogarithmic approximation ratio for a natural NP-hard optimization problem. We show that for every fixed ε>0, the GROUP-STEINER-TREE problem admits no efficient log2-ε k approximation, where k denotes the number of groups (or, alternatively, the input size), unless NP has quasi polynomial Las-Vegas algorithms. This hardness result holds even for input graphs which are Hierarchically Well-Separated Trees, introduced by Bartal [FOCS, 1996]. For these… 

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