English

Hitting Diamonds and Growing Cacti

Data Structures and Algorithms 2015-05-14 v2 Discrete Mathematics

Abstract

We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is \Theta(\log n), where n denotes the number of vertices in the graph.

Keywords

Cite

@article{arxiv.0911.4366,
  title  = {Hitting Diamonds and Growing Cacti},
  author = {Samuel Fiorini and Gwenaël Joret and Ugo Pietropaoli},
  journal= {arXiv preprint arXiv:0911.4366},
  year   = {2015}
}

Comments

v2: several minor changes.

R2 v1 2026-06-21T14:14:52.579Z