Abstract
We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labbé and Maffioli (Operations Research, vol. 48, no. 6, pp. 866–877, 2000).
In this paper, we compute a lower bound on the number of edges in a feasible solution, we show that the problem is strongly NP-complete for any fixed K, and we derive a new class of facet defining inequalities. Numerical results obtained with a branch-and-cut algorithm using these inequalities show their effectiveness for solving the problem.
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Fortz, B., Labbé, M. Two-Connected Networks with Rings of Bounded Cardinality. Computational Optimization and Applications 27, 123–148 (2004). https://doi.org/10.1023/B:COAP.0000008649.61438.6b
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DOI: https://doi.org/10.1023/B:COAP.0000008649.61438.6b