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

Data Structures and Algorithms 2016-04-28 v1

Abstract

We demonstrate that the integrality gap of the natural cut-based LP relaxation for the directed Steiner tree problem is O(logk)O(\log k) in quasi-bipartite graphs with kk 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.

Keywords

Cite

@article{arxiv.1604.08132,
  title  = {A Logarithmic Integrality Gap Bound for Directed Steiner Tree in Quasi-bipartite Graphs},
  author = {Zachary Friggstad and Jochen Koenemann and Mohammad Shadravan},
  journal= {arXiv preprint arXiv:1604.08132},
  year   = {2016}
}