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Acquiring Maps of Interrelated Conjectures on Sharp Bounds

Authors Nicolas Beldiceanu, Jovial Cheukam-Ngouonou, Rémi Douence, Ramiz Gindullin, Claude-Guy Quimper

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ACM Subject Classification
  • Computing methodologies → Heuristic function construction
  • Mathematics of computing → Combinatorial optimization
Keywords
  • Acquisition of conjectures
  • digraphs
  • bounds

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Abstract

To automate the discovery of conjectures on combinatorial objects, we introduce the concept of a map of sharp bounds on characteristics of combinatorial objects, that provides a set of interrelated sharp bounds for these combinatorial objects. We then describe a Bound Seeker, a CP-based system, that gradually acquires maps of conjectures. The system was tested for searching conjectures on bounds on characteristics of digraphs: it constructs sixteen maps involving 431 conjectures on sharp lower and upper-bounds on eight digraph characteristics.

Cite As Get BibTex

Nicolas Beldiceanu, Jovial Cheukam-Ngouonou, Rémi Douence, Ramiz Gindullin, and Claude-Guy Quimper. Acquiring Maps of Interrelated Conjectures on Sharp Bounds. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CP.2022.6

Author Details

Nicolas Beldiceanu
  • IMT Atlantique, LS2N (TASC), Nantes, France
Jovial Cheukam-Ngouonou
  • IMT Atlantique, LS2N (TASC), Nantes, France, and Université Laval, Québec, Canada
Rémi Douence
  • IMT Atlantique, LS2N, Inria, (Gallinette), Nantes, France
Ramiz Gindullin
  • IMT Atlantique, LS2N (TASC), Nantes, France
Claude-Guy Quimper
  • Université Laval, Québec, Canada

Funding

  • Beldiceanu, Nicolas: partially founded by the EU-funded ASSISTANT project no. 101000165.
  • Cheukam-Ngouonou, Jovial: founded by the ANR AI@IMT project and by Laval University.
  • Gindullin, Ramiz: founded by the EU-funded ASSISTANT project.

Acknowledgements

Thanks to Hervé Grall for his participation in the definition of the map concept, and to Samir Loudni and Helmut Simonis for their comments on a preliminary version of this paper.

Supplementary Materials

References

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