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On residual approximation in solution extension problems

Author

Listed:
  • Mathias Weller

    (LIRMM - CNRS UMR 5506)

  • Annie Chateau

    (LIRMM - CNRS UMR 5506)

  • Rodolphe Giroudeau

    (LIRMM - CNRS UMR 5506)

  • Jean-Claude König

    (LIRMM - CNRS UMR 5506)

  • Valentin Pollet

    (LIRMM - CNRS UMR 5506)

Abstract

The solution extension variant of a problem consists in, being given an instance and a partial solution, finding the best solution comprising the given partial solution. Many problems have been studied with a similar approach. For instance the Pre-Coloring Extension problem, the clustered variant of the Travelling Salesman problem, or the General Routing Problem are in a way typical examples of solution extension variant problems. Motivated by practical applications of such variants, this work aims to explore different aspects around extension on classical optimization problems. We define residue-approximations as algorithms whose performance ratio on the non-prescribed part can be bounded, and corresponding complexity classes. Using residue-approximation, we classify problems according to their residue-approximability, exhibit distinct behaviors and give several examples and first interesting results.

Suggested Citation

  • Mathias Weller & Annie Chateau & Rodolphe Giroudeau & Jean-Claude König & Valentin Pollet, 2018. "On residual approximation in solution extension problems," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1195-1220, November.
  • Handle: RePEc:spr:jcomop:v:36:y:2018:i:4:d:10.1007_s10878-017-0202-5
    DOI: 10.1007/s10878-017-0202-5
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    References listed on IDEAS

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    1. Michel Gendreau & Gilbert Laporte & Alain Hertz, 1997. "An Approximation Algorithm for the Traveling Salesman Problem with Backhauls," Operations Research, INFORMS, vol. 45(4), pages 639-641, August.
    2. Christos H. Papadimitriou & Mihalis Yannakakis, 1993. "The Traveling Salesman Problem with Distances One and Two," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 1-11, February.
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    Cited by:

    1. Pourhejazy, Pourya & Zhang, Dali & Zhu, Qinghua & Wei, Fangfang & Song, Shuang, 2021. "Integrated E-waste transportation using capacitated general routing problem with time-window," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).

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