Covering a graph with cycles

In several areas of engineering and telecommunications, it is necessary to determine a least cost cover of a graph by means of cycles. We propose a highly efficient yet simple heuristic for this difficult problem. On test problems it consistently produces optimal or near optimal solutions. This article describes a lower bounding procedure and heuristics for the Cycle Cover Problem which consists of determining a least cost cover of an undirected graph with simple cycles. Applications of this problem arise in network design and in telecommunications. Computational results demonstrate the quality of the proposed heuristics. On 100 vertex graphs, the best of these consistently produces optimal or quasi-optimal solutions.