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On a Geometric Graph-Covering Problem Related to Optimal Safety-Landing-Site Location

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Combinatorial Optimization (ISCO 2024)

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Abstract

We develop a set-cover based integer-programming approach to an optimal safety-landing-site location arising in the design of urban air-transportation networks. We link our minimum-weight set-cover problems to efficiently-solvable cases of minimum-weight set covering that have been studied. We were able to solve large random instances to optimality using our modeling approach. We carried out strong fixing, a technique that generalizes reduced-cost fixing, and which we found to be very effective in reducing the size of our integer-programming instances.

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Notes

  1. 1.

    a 0/1 matrix is totally balanced if it has no square submatrix (of any order) with two ones per row and per column, thus a subclass of balanced 0/1 matrices; see [11].

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Acknowledgments

This work was supported by NSF grant DMS-1929284 while C. D’Ambrosio, M. Fampa and J. Lee were in residence at ICERM (the Institute for Computational and Experimental Research in Mathematics; Providence, RI) during the Discrete Optimization program, 2023. C. D’Ambrosio was supported by the Chair “Integrated Urban Mobility”, backed by L’X - École Polytechnique and La Fondation de l’École Polytechnique (The Partners of the Chair accept no liability related to this publication, for which the chair holder is solely liable). M. Fampa was supported by CNPq grant 307167/2022-4. J. Lee was supported by the Gaspard Monge Visiting Professor Program, École Polytechnique, and from ONR grant N00014-21-1-2135. F. Sinnecker was supported on a masters scholarship from CNPq. J. Lee and M. Fampa acknowledge (i) interesting conversations at ICERM with Zhongzhu Chen on variable fixing, and (ii) some helpful information from Tobias Achterberg on Gurobi presolve.

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D’Ambrosio, C., Fampa, M., Lee, J., Sinnecker, F. (2024). On a Geometric Graph-Covering Problem Related to Optimal Safety-Landing-Site Location. In: Basu, A., Mahjoub, A.R., Salazar González, J.J. (eds) Combinatorial Optimization. ISCO 2024. Lecture Notes in Computer Science, vol 14594. Springer, Cham. https://doi.org/10.1007/978-3-031-60924-4_2

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