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Backtrack Search for Parallelisms of Projective Spaces

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Combinatorial Algorithms (IWOCA 2021)

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Abstract

A spread in \(\mathrm{PG}(n,q)\) is a set of lines which partition the point set. A partition of the set of lines by spreads is called a parallelism. The numerous relations and applications of parallelisms determine a significant interest in the methods for their construction. We consider two different backtrack search algorithms which can be used for that purpose. The first one implies search on a set of spreads, and the second - on the lines of the projective space. The authors have used them for the classification of parallelisms invariant under definite automorphism groups. The present paper concerns the applicability of each of the two algorithms to cases with different peculiarities, and some ways to modify them for usage on parallel computers. Suitable examples are given.

The research of both authors is partially supported by the Bulgarian National Science Fund under Contract No KP-06-N32/2-2019.

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Acknowledgements

For testing the algorithms from Sect. 4 the authors acknowledge the provided access to the e-infrastructure of the NCHDC – part of the Bulgarian National Roadmap on RIs, with the financial support by the Grant No D01-221/03.12.2018.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetlana Topalova & Stela Zhelezova

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  1. Svetlana Topalova
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  2. Stela Zhelezova
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Correspondence to Stela Zhelezova .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Ottawa, Ottawa, ON, Canada

    Lucia Moura

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Topalova, S., Zhelezova, S. (2021). Backtrack Search for Parallelisms of Projective Spaces. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_38

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  • DOI: https://doi.org/10.1007/978-3-030-79987-8_38

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