Exact approaches for the Connected Vertex Cover problem

TL;DR

This paper introduces the first exact mixed-integer formulations for the Connected Vertex Cover problem, along with a branch and bound algorithm, demonstrating the formulations' superior performance in computational experiments.

Contribution

It presents the first compact mixed-integer extended formulations for CVC and compares their effectiveness against a branch and bound approach.

Findings

Formulations outperform branch and bound in experiments

First mixed-integer formulations proposed for CVC

Formulations can be adapted to related problems like Tree Cover

Abstract

Given a graph $G$, the Connected Vertex Cover problem (CVC) asks to find a minimum cardinality vertex cover of $G$ 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.