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

  • Anne BerryEmail author
  • Alain Gutierrez
  • Marianne Huchard
  • Amedeo Napoli
  • Alain Sigayret


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.


Binary Relation Linear Extension Concept Lattice Software Product Line Formal Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Anne Berry
    • 1
    Email author
  • Alain Gutierrez
    • 2
  • Marianne Huchard
    • 2
  • Amedeo Napoli
    • 3
  • Alain Sigayret
    • 1
  1. 1.LIMOS (CNRS UMR 6158 - Université Clermont-Ferrand II)Clermont-FerrandFrance
  2. 2.LIRMM (CNRS UMR 5506 – Université de Montpellier II)MontpellierFrance
  3. 3.LORIA (CNRS UMR 7503 – Inria Nancy Grand Est – Université de Lorraine)Vandoeuvre-lès-NancyFrance

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