Abstract
In this paper we study the problem of generating all keys of a formal context as well as a hypergraph. We show that computing the maximum size of a key is NP-complete. Consequently, there is no polynomial time algorithm that decides if a hypergraph is k-conformal, unless P=NP. We also present an algorithmic framework based on decomposition to enumerates all keys of a hypergraph. As example we propose a decomposition of a hypergraph into conformal hypergraphs. Computing a minimal decomposition of an arbitrary hypergraph into conformal hypergraphs remains open in this paper.
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Colomb, P., Nourine, L. (2008). About Keys of Formal Context and Conformal Hypergraph. In: Medina, R., Obiedkov, S. (eds) Formal Concept Analysis. ICFCA 2008. Lecture Notes in Computer Science(), vol 4933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78137-0_10
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DOI: https://doi.org/10.1007/978-3-540-78137-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78136-3
Online ISBN: 978-3-540-78137-0
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