A tight example for approximation ratio 5 for covering small cuts by the primal-dual method
Data Structures and Algorithms
2025-12-23 v2
Abstract
In the Small Cuts Cover problem we seek to cover by a min-cost edge-set the set family of cuts of size/capacity of a graph. Recently, Simmons showed that the primal-dual algorithm of Williamson, Goemans, Mihail, and Vazirani achieves approximation ratio for this problem, and asked whether this bound is tight. We will answer this question positively, by providing an example in which the ratio between the solution produced by the primal-dual algorithm and the optimum is arbitrarily close to .
Keywords
Cite
@article{arxiv.2512.08350,
title = {A tight example for approximation ratio 5 for covering small cuts by the primal-dual method},
author = {Zeev Nutov},
journal= {arXiv preprint arXiv:2512.08350},
year = {2025}
}