# Polylogarithmic inapproximability

```@inproceedings{Halperin2003PolylogarithmicI,
title={Polylogarithmic inapproximability},
author={Eran Halperin and Robert Krauthgamer},
booktitle={STOC '03},
year={2003}
}```
• Published in STOC '03 9 June 2003
• Computer Science, Mathematics
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…
231 Citations

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SODA '03
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An Ω(log2k) lower bound on the integrality ratio of the flow-based relaxation for the Group Steiner Tree problem is presented, where k denotes the number of groups; this holds even for input graphs that are Hierarchically Well-Separated Trees, in which case this lower bound is tight.

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