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 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.