Beating the 2-approximation factor for global bicut

  • Kristóf Bérczi
  • Karthekeyan Chandrasekaran
  • Tamás Király
  • Euiwoong Lee
  • Chao Xu
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Abstract

In the fixed-terminal bicut problem, the input is a directed graph with two specified nodes s and t and the goal is to find a smallest subset of edges whose removal ensures that s cannot reach t and t cannot reach s. In the global bicut problem, the input is a directed graph and the goal is to find a smallest subset of edges whose removal ensures that there exist two nodes s and t such that s cannot reach t and t cannot reach s. Fixed-terminal bicut and global bicut are natural extensions of \(\{s,t\}\)-min cut and global min-cut respectively, from undirected graphs to directed graphs. Fixed-terminal bicut is NP-hard, admits a simple 2-approximation, and does not admit a \((2-\epsilon )\)-approximation for any constant \(\epsilon >0\) assuming the unique games conjecture. In this work, we show that global bicut admits a \((2-1/448)\)-approximation, thus improving on the approximability of the global variant in comparison to the fixed-terminal variant.

Keywords

Digraphs Bicut Linear cut k-cut 

Mathematics Subject Classification

05C85 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments in improving the presentation of this work.

Supplementary material

10107_2018_1270_MOESM1_ESM.pdf (891 kb)
Supplementary material 1 (pdf 890 KB)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  • Kristóf Bérczi
    • 1
  • Karthekeyan Chandrasekaran
    • 2
  • Tamás Király
    • 1
  • Euiwoong Lee
    • 3
  • Chao Xu
    • 2
  1. 1.MTA-ELTE Egerváry Research Group, Department of Operations ResearchEötvös Loránd UniversityBudapestHungary
  2. 2.University of IllinoisUrbana-ChampaignUSA
  3. 3.Carnegie Mellon UniversityPittsburghUSA

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