Optimal constant in Steiner forest packing

Determine the optimal constant in the Steiner forest packing guarantee that follows from pairwise connectivity, improving the currently known bound of approximately f/16 disjoint forests toward the required f+1 forests, and determine the corresponding bound for Steiner trees.

Background

The paper’s construction relies on packing Steiner forests in a fault-tolerant connectivity preserver. Existing results provide only a constant-factor fraction of the desired number of forests in the general setting, while the exact packing threshold is unknown even for Steiner trees. The authors avoid this unresolved issue through an edge-doubling and Eulerian-graph argument, but identify the packing constant as an independent open problem.