An Optimal Rounding for Half-Integral Weighted Minimum Strongly Connected Spanning Subgraph

Abstract

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 $2-f$.

References in corpus (1)

• Coloring Down: $3/2$-approximation for special cases of the weighted tree augmentation problem