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Boosting isomorphic model filtering with invariants

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Abstract

The enumeration of finite models is very important to the working discrete mathematician (algebra, graph theory, etc) and hence the search for effective methods to do this task is a critical goal in discrete computational mathematics. However, it is hindered by the possible existence of many isomorphic models, which usually only add noise. Typically, they are filtered out a posteriori, a step that might take a long time just to discard redundant models. This paper proposes a novel approach to split the generated models into mutually non-isomorphic blocks. To do that we use well-designed hand-crafted invariants as well as randomly generated invariants. The blocks are then tackled separately and possibly in parallel. This approach is integrated into Mace4 (the most popular tool among mathematicians) where it shows tremendous speed-ups for a large variety of algebraic structures.

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Notes

  1. Some preliminary ideas and results have been presented in [2]. This paper adds more invariants including randomly generated invariants and proves their validity. It also reports substantially more experimental results and drills deeper into related work.

  2. We conjecture that the problem is NP-hard; it resembles K-means clustering, which is NP-hard [1].

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Funding

João Araújo: The results were supported by the Fundação para a Ciência e a Tecnologia, through the projects UIDB/00297-/2020 (CMA), PTDC/MAT-PUR/31174/2017, UIDB/04621/2020 and UIDP/04621/2020.

Mikoláš Janota: The results were supported by the Ministry of Education, Youth and Sports within the dedicated program ERC CZ under the project POSTMAN no. LL1902. This scientific article is part of the RICAIP project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 857306.

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Authors and Affiliations

  1. Universidade Nova de Lisboa, Lisbon, Portugal

    João Araújo

  2. Universidade Aberta, Lisbon, Portugal

    Choiwah Chow

  3. Czech Technical University in Prague, Prague, Czechia

    Mikoláš Janota

Authors
  1. João Araújo
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  2. Choiwah Chow
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  3. Mikoláš Janota
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Correspondence to Choiwah Chow.

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Araújo, J., Chow, C. & Janota, M. Boosting isomorphic model filtering with invariants. Constraints 27, 360–379 (2022). https://doi.org/10.1007/s10601-022-09336-x

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