# 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…

## 231 Citations

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### Integrality ratio for group Steiner trees and directed steiner trees

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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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