# A branch-and-cut algorithm for the maximum covering cycle problem

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## Abstract

In many applications, such as telecommunications and routing, we seek for cost-effective infrastructure or operating layouts so that many nodes (e.g., customers) of a support network (typically modeled by a graph) are covered by, or at least are easily reachable from, such a layout. In this paper, we study the maximum covering cycle problem. In this problem we are given a non-complete graph, and the goal is to find a cycle, such that the number of nodes which are either on the cycle or are adjacent to the cycle is maximized. We design a branch-and-cut framework for solving the problem. The framework contains valid inequalities, lifted inequalities and a primal heuristic. In a computational study, we compare our framework to previous work available for this problem. The results reveal that our approach significantly outperforms the previous approach. In particular, all available instances from the literature could be solved to optimality with our approach, most of them within a few seconds.

## Keywords

Covering problems Branch-and-cut Optimal cycle problems Domination problems## Notes

### Acknowledgements

E. Álvarez-Miranda acknowledges the support of the Chilean Council of Scientific and Technological Research, CONICYT, through the FONDECYT Grant N.1180670 and through the Complex Engineering Systems Institute (ICM-FIC:P-05-004-F, CONICYT:FB0816). The research of M. Sinnl was supported by the Austrian Research Fund (FWF, Project P 26755-N19).

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