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Modelling and solving the perfect edge domination problem

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Abstract

A formulation is proposed for the perfect edge domination problem and some exact algorithms based on it are designed and tested. So far, perfect edge domination has been investigated mostly in computational complexity terms. Indeed, we could find no previous explicit mathematical formulation or exact algorithm for the problem. Furthermore, testing our algorithms also represented a challenge. Standard randomly generated graphs tend to contain a single perfect edge dominating solution, i.e., the trivial one, containing all edges in the graph. Accordingly, some quite elaborated procedures had to be devised to have access to more challenging instances. A total of 736 graphs were thus generated, all of them containing feasible solutions other than the trivial ones. Every graph giving rise to a weighted and a non weighted instance, all instances solved to proven optimality by two of the algorithms tested.

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Acknowledgements

The authors wish to thank the two anonymous referees for various suggestions that helped improve this paper. V. L. do Forte: Vinicius Leal do Forte was partially funded by CNPq. M. C. Lin: Min Chih Lin was partially funded by UBACyT Grant 20020120100058, and PICT ANPCyT Grants 2010-1970 and 2013-2205. A. Lucena: Abilio Lucena was partially funded by CNPq grant 307026/2013-2. N. Maculan: Nelson Maculan was partially funded by CNPq. V. A. Moyano: Veronica A. Moyano was partially funded by UBACyT Grant 20020120100058, and PICT ANPCyT Grants 2010-1970 and 2013-2205 J. L. Szwarcfiter: Jayme L. Szwarcfiter was partially funded by CNPq.

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Correspondence to Nelson Maculan.

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do Forte, V.L., Lin, M.C., Lucena, A. et al. Modelling and solving the perfect edge domination problem. Optim Lett 14, 369–394 (2020). https://doi.org/10.1007/s11590-018-1335-x

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Keywords

  • Perfect edge domination
  • Exact algorithms
  • Instance generation
  • Computational results