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

Data Structures and Algorithms 2020-11-13 v1

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 1.51.5 cost. This rounding matches a known 1.51.5 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>0f > 0 can be rounded at a multiplicative cost of 2f2 - f.

Keywords

Cite

@article{arxiv.2011.06108,
  title  = {An Optimal Rounding for Half-Integral Weighted Minimum Strongly Connected Spanning Subgraph},
  author = {D Ellis Hershkowitz and Gregory Kehne and R. Ravi},
  journal= {arXiv preprint arXiv:2011.06108},
  year   = {2020}
}
R2 v1 2026-06-23T20:06:49.490Z