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On the Enumeration of Non-dominated Spanning Trees with Imprecise Weights

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14294))

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Abstract

Many works within robust combinatorial optimisation consider interval-valued costs or constraints. While most of these works focus on finding unique solutions such as minimax ones, a few consider the problem of characterising a set of non-dominated optimal solutions. This paper is situated within this line of work, and consider the problem of exactly enumerating the set of non-dominated spanning trees under interval-valued costs. We show in particular that each tree in this set can be obtained through a polynomial procedure, and provide an efficient algorithm to achieve the enumeration.

Due to paucity of space, proofs has been omitted. The full version is available here: https://hal.utc.fr/hal-04155185.

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Notes

  1. 1.

    We have provided proofs in the appendix for review purposes, as including them would exceed page limits. Appendices will not be part of the final version.

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Authors and Affiliations

  1. Université de Technologie de Compiègne, CNRS, Heudiasyc (Heuristics and Diagnosis of Complex Systems), 60319 - 60203, Compiègne, France

    Tom Davot, Sébastien Destercke & David Savourey

Authors
  1. Tom Davot
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  2. Sébastien Destercke
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  3. David Savourey
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Correspondence to Tom Davot .

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Editors and Affiliations

  1. CRIL CNRS University Artois, Lens Cedex, France

    Zied Bouraoui

  2. CRIL CNRS University Artois, Lens Cedex, France

    Srdjan Vesic

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Davot, T., Destercke, S., Savourey, D. (2024). On the Enumeration of Non-dominated Spanning Trees with Imprecise Weights. In: Bouraoui, Z., Vesic, S. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2023. Lecture Notes in Computer Science(), vol 14294. Springer, Cham. https://doi.org/10.1007/978-3-031-45608-4_26

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  • DOI: https://doi.org/10.1007/978-3-031-45608-4_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45607-7

  • Online ISBN: 978-3-031-45608-4

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