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arXiv · 2011.06108

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

D Ellis Hershkowitz·Gregory Kehne·R. Ravi
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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 $2 - f$.

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D Ellis Hershkowitz, Gregory Kehne, R. Ravi. 2020-11-11. An Optimal Rounding for Half-Integral Weighted Minimum Strongly Connected Spanning Subgraph. https://arxiv.org/abs/2011.06108

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