Beating the 2-approximation factor for global bicut

Abstract

In the fixed-terminal bicut problem, the input is a directed graph with two specified nodes and the goal is to find a smallest subset of edges whose removal ensures that the two specified nodes cannot reach each other. 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 that cannot reach each other. 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 −)-approximation for any constant > 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.