# A Logarithmic Integrality Gap Bound for Directed Steiner Tree in Quasi-bipartite Graphs

```@article{Friggstad2016ALI,
title={A Logarithmic Integrality Gap Bound for Directed Steiner Tree in Quasi-bipartite Graphs},
journal={ArXiv},
year={2016},
volume={abs/1604.08132}
}```
• Published 2016
• Mathematics, Computer Science
• ArXiv
• We demonstrate that the integrality gap of the natural cut-based LP relaxation for the directed Steiner tree problem is \$O(\log k)\$ in quasi-bipartite graphs with \$k\$ terminals. Such instances can be seen to generalize set cover, so the integrality gap analysis is tight up to a constant factor. A novel aspect of our approach is that we use the primal-dual method; a technique that is rarely used in designing approximation algorithms for network design problems in directed graphs.
4 Citations

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