On some path problems on oriented hypergraphs

Nguyen, Sang; Pretolani, Daniele; Markenzon, Lilian

doi:10.1051/ita/1998321-300011

Cited by 8 publications

(10 citation statements)

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“…Such relationships appear in different areas of Computer Science such as database systems (Ausiello et al, 1985), expert systems (Ramaswamy et al, 1997), parallel programming (Nguyen et al, 1998), scheduling (Lin & Sarrafzadeh, 1995;Gallo & Scutellà, 2002), routing in dynamic networks (Pretolani, 2000) and, more recently, data mining (Chawla et al, 2004) and bioinformatics (Krishnamurthy et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

Directed hypergraph planarity

Guedes

Markenzon

2005

Pesqui. Oper.

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Directed hypergraphs are generalizations of digraphs and can be used to model binary relations among subsets of a given set. Planarity of hypergraphs was studied by Johnson and Pollak; in this paper we extend the planarity concept to directed hypergraphs. It is known that the planarity of a digraph relies on the planarity of its underlying graph. However, for directed hypergraphs, this property do not apply and we propose a new approach which generalizes the usual concept. We also show that the complexity of the recognition of a directed hypergraph as planar is linear on the size of the hypergraph.Keywords: directed hypergraphs; planarity; algorithms. ResumoHipergrafos direcionados são generalizações de digrafos, e são utilizados na modelagem de relações binárias entre subconjuntos de um dado conjunto. O problema da planaridade em hipergrafos foi estudado por Johnson e Pollak; neste trabalho estendemos o conceito de planaridade para hipergrafos direcionados. É noção conhecida que a planaridade de hipergrafos depende da planaridade de seu grafo subjacente. Entretanto, para hipergrafos direcionados, esta propriedade não pode ser aplicada e propomos uma nova abordagem que generaliza o conceito tradicional. Mostramos também que a complexidade de testar a planaridade de um hipergrafo direcionado é linear no tamanho do hipergrafo.Palavras-chave: hipergrafos direcionados; planaridade; algoritmos.

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Section: Introductionmentioning

confidence: 99%

Directed hypergraph planarity

Guedes

Markenzon

2005

Pesqui. Oper.

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“…(2) An extended version of the function Bvisit(·, ·) [18,31] for completely traversing a directed hypergraph similar to how Breadth-first search works.…”

Section: Chapter 2 Preliminaries I: Directed Graphs and Hypergraphsmentioning

confidence: 99%

“…B-connectivity has popularized the use of directed hypergraphs to represent n-ary relations in problems related to relational databases, propositional logic, biological networks and ontologies [18,31,22,38]. In B-connectivity, the tail nodes of a hyperedge have a prominent role because only when all of them are reached, it is possible to reach the head nodes.…”

Section: Directed Hypergraphsmentioning

confidence: 99%

“…Besides B-connectivity, there are different notions of connectivity in directed hypergraphs. Among others, F-connectivity and BF-connectivity are also very popular in the literature [18,31]. Like tail nodes in B-connectivity, these notions stress the importance of head nodes in a directed hyperedge.…”

Section: Directed Hypergraphsmentioning

confidence: 99%

“…There are algorithms that can identify which are the nodes that are connected from a particular node using a specific connectivity notion (L-connectivity [40], B-connectivity, Fconnectivity and BF-connectivity [18,31]). This is for computing the connected component of a node in a directed hypergraph.…”

Section: Breadth-first Search Algorithmmentioning

confidence: 99%

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