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

Olivier Hudry 1, 2
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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Submitted on : Friday, September 13, 2019 - 3:33:19 PM
Last modification on : Tuesday, October 19, 2021 - 11:15:21 AM

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  • HAL Id : hal-02286265, version 1

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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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