Hermes: an efficient algorithm for building Galois sub-hierarchies
Identifieur interne : 001931 ( Main/Merge ); précédent : 001930; suivant : 001932Hermes: an efficient algorithm for building Galois sub-hierarchies
Auteurs : Anne Berry [France] ; Marianne Huchard [France] ; Amedeo Napoli [France] ; Alain Sigayret [France]Source :
Descripteurs français
Abstract
Given a binary relation R on a set O of objects and a set A of attributes, the Galois sub-hierarchy (also called AOC-poset) is the partial order on the introducers of objects and attributes in the corresponding concept lattice. We present a new efficient algorithm for building a Galois sub-hierarchy which runs in O(min{nm, n ^{\alpha}}), where n is the number of objects or attributes, m is the size of the relation, and n ^{\alpha} is the time required to perform matrix multiplication (currently \alpha = 2.376).
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<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
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<country>France</country>
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<author><name sortKey="Sigayret, Alain" sort="Sigayret, Alain" uniqKey="Sigayret A" first="Alain" last="Sigayret">Alain Sigayret</name>
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<country>France</country>
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</sourceDesc>
</fileDesc>
<profileDesc><textClass><keywords scheme="mix" xml:lang="fr"><term>AOC-concept poset</term>
<term>Concept lattice</term>
<term>Galois Sub-Hierarchy</term>
<term>Galois lattice</term>
<term>algorithm</term>
</keywords>
</textClass>
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</teiHeader>
<front><div type="abstract" xml:lang="en">Given a binary relation R on a set O of objects and a set A of attributes, the Galois sub-hierarchy (also called AOC-poset) is the partial order on the introducers of objects and attributes in the corresponding concept lattice. We present a new efficient algorithm for building a Galois sub-hierarchy which runs in O(min{nm, n ^{\alpha}}), where n is the number of objects or attributes, m is the size of the relation, and n ^{\alpha} is the time required to perform matrix multiplication (currently \alpha = 2.376).</div>
</front>
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