The Reverse Doubling Construction

Viaud, Jean-François; Bertet, Karell; Demko, Christophe; Missaoui, Rokia

doi:10.5220/0005613203500357

Cited by 3 publications

(1 citation statement)

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“…The concept of splitting lattices or closure systems is an old question and remains an active topic in several areas in mathematics and computer science. Among the common ways to split a lattice are the subdirect decomposition, the duplication (or doubling) of convex sets [BC02,VBDM15a], and other summarised decomposition in [GW99, GW12, Grä11, KVD05]. The former has been early considered by Birkhoff in [Bir44] where his representation theorem "Every algebra is a subdirect product of its subdirectly irreducible homomorphic images" is stated.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Decompositions of dihypergraphs

Nourine¹,

Vilmin²

2020

Preprint

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In this paper we are interested in decomposing a dihypergraph H = (V, E) into simpler dihypergraphs, that can be handled more efficiently. We study the properties of dihypergraphs that can be hierarchically decomposed into trivial dihypergraphs, i.e., vertex hypergraph. The hierarchical decomposition is represented by a full labelled binary tree called H-tree, in the fashion of hierarchical clustering. We present a polynomial time and space algorithm to achieve such a decomposition by producing its corresponding H-tree. However, there are dihypergraphs that cannot be completely decomposed into trivial components. Therefore, we relax this requirement to more indecomposable dihypergraphs called H-factors, and discuss applications of this decomposition to closure systems and lattices.

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Section: Introductionmentioning

confidence: 99%