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

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(min{nm, nα}), where n is the number of objects plus the number of attributes, m is the size of the relation, and nα 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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