Polynomial-time approximability of the Two-Edge Connected Directed Steiner Tree problem

Investigate the polynomial-time approximability of the Two-Edge Connected Directed Steiner Tree problem, which asks for a minimum-cost subgraph that provides two edge-disjoint directed paths from the root to each terminal; in particular, ascertain whether a polynomial-time polylogarithmic approximation can be achieved for this problem.

Background

The Two-Edge Connected Directed Steiner Tree (2-EC DST) problem generalizes DST by requiring two edge-disjoint directed paths from the root to each terminal. The authors note that quasi-polynomial-time algorithms achieve polylogarithmic approximations for λ=2, but the existence of comparable polynomial-time guarantees is not established. They point to their Decompose-and-Round framework as a plausible approach for progress.

In the conclusion, the authors explicitly identify the 2-EC DST as an open question for network design researchers, highlighting its status and relevance for future work.