NP-hardness of the computation of a median equivalence relation in classification (Régnier’s problem) - Archive ouverte HAL Access content directly
Journal Articles Mathematics and Social Sciences Year : 2012

NP-hardness of the computation of a median equivalence relation in classification (Régnier’s problem)

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Abstract

Given a collection C of equivalence relations (or partitions), Régnier’s problem consists in computing an equivalence relation which minimizes the remoteness from C. The remoteness is based on the symmetric difference distance and measures the number of disagreements between C and the considered equivalence relation. Such an equivalence relation minimizing the remoteness is called a median equivalence relation of C. We prove the NP-hardness of Régnier’s problem, i.e. the computation of a median equivalence relation of a collection C of equivalence relations, at least when the number of equivalence relations of C is large enough.
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Dates and versions

hal-02286265 , version 1 (13-09-2019)

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  • HAL Id : hal-02286265 , version 1

Cite

Olivier Hudry. NP-hardness of the computation of a median equivalence relation in classification (Régnier’s problem). Mathematics and Social Sciences, 2012, 197, pp.83-97. ⟨hal-02286265⟩
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