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arXiv · 2203.09868

Exact approaches for the Connected Vertex Cover problem

Manuel Aprile
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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.

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Manuel Aprile. 2022-03-18. Exact approaches for the Connected Vertex Cover problem. https://arxiv.org/abs/2203.09868

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