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Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation

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Abstract

Given a relation 𝓡 ⊆ 𝓞 × 𝓐 on a set 𝓞 of objects and a set 𝓐 of attributes, the AOC-poset (Attribute/Object Concept poset), is the partial order defined on the “introducers” of objects and attributes in the corresponding concept lattice. In this paper, we present Hermes, a simple and efficient algorithm for building an AOC-poset which runs in O(m i n{n m, n α}), where n is the number of objects plus the number of attributes, m is the size of the relation, and n α is the time required to perform matrix multiplication (currently α = 2.376). Finally, we compare the runtime of Hermes with the runtime of other algorithms computing the AOC-poset: Ares, Ceres and Pluton. We characterize the cases where each algorithm is the more relevant.

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Authors and Affiliations

  1. LIMOS (CNRS UMR 6158 - Université Clermont-Ferrand II), Clermont-Ferrand, France

    Anne Berry & Alain Sigayret

  2. LIRMM (CNRS UMR 5506 – Université de Montpellier II), Montpellier, France

    Alain Gutierrez & Marianne Huchard

  3. LORIA (CNRS UMR 7503 – Inria Nancy Grand Est – Université de Lorraine), Vandoeuvre-lès-Nancy, France

    Amedeo Napoli

Authors
  1. Anne Berry
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  2. Alain Gutierrez
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  3. Marianne Huchard
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  4. Amedeo Napoli
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  5. Alain Sigayret
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Correspondence to Anne Berry.

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Berry, A., Gutierrez, A., Huchard, M. et al. Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation. Ann Math Artif Intell 72, 45–71 (2014). https://doi.org/10.1007/s10472-014-9418-6

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