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 tandt 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 tandt 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.
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The authors would like to thank the anonymous reviewers for their helpful comments in improving the presentation of this work.
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A preliminary version of this work appeared in the 20th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2017).
Kristóf Bérczi and Tamás Király are supported by the Hungarian National Research, Development and Innovation Office – NKFIH Grants K109240 and K120254 and by the ÚNKP-17-4 New National Excellence Program of the Ministry of Human Capacities.
Chao Xu is supported in part by NSF Grant CCF-1526799.
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Bérczi, K., Chandrasekaran, K., Király, T. et al. Beating the 2-approximation factor for global bicut. Math. Program. 177, 291–320 (2019). https://doi.org/10.1007/s10107-018-1270-8
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DOI: https://doi.org/10.1007/s10107-018-1270-8