English

Exact approaches for the Connected Vertex Cover problem

Data Structures and Algorithms 2023-02-20 v2 Discrete Mathematics Combinatorics

Abstract

Given a graph GG, the Connected Vertex Cover problem (CVC) asks to find a minimum cardinality vertex cover of GG that induces a connected subgraph. In this paper we describe some approaches to solve the CVC problem exactly. First, we give compact mixed-integer extended formulations for CVC: these are the first formulations proposed for this problem, and can be easily adapted to variations of the problem such as Tree Cover. Second, we describe a simple branch and bound algorithm for the CVC problem. Finally, we implement our algorithm and compare its performance against our best formulation: contrary to what usually happens for the classical Vertex Cover problem, our formulation outperforms the branch and bound algorithm.

Keywords

Cite

@article{arxiv.2203.09868,
  title  = {Exact approaches for the Connected Vertex Cover problem},
  author = {Manuel Aprile},
  journal= {arXiv preprint arXiv:2203.09868},
  year   = {2023}
}
R2 v1 2026-06-24T10:18:13.628Z