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

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