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arXiv · 1604.08132

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

Zachary Friggstad·Jochen Koenemann·Mohammad Shadravan
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Abstract

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.

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Zachary Friggstad, Jochen Koenemann, Mohammad Shadravan. 2016-04-27. A Logarithmic Integrality Gap Bound for Directed Steiner Tree in Quasi-bipartite Graphs. https://arxiv.org/abs/1604.08132

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