An optimal rounding for half-integral weighted minimum strongly connected spanning subgraph

•We give a 1.5-approximation for half-integral weighted MSCSS.•Our 1.5-approximation matches a known integrality gap lower bound.•We give a 2−f approximation if LP values are bounded below by f. In the weighted minimum strongly connected spanning subgraph (WMSCSS ) problem we must purchase a minimum-cost strongly connected spanning subgraph of a digraph. We show that half-integral linear program (LP) solutions for WMSCSS can be efficiently rounded to integral solutions at a multiplicative 1.5 cost. This rounding matches a known 1.5 integrality gap lower bound for a half-integral instance. More generally, we show that LP solutions whose non-zero entries are at least a value f>0 can be rounded at a multiplicative cost of 2−f.