Hypergraph planarity and the complexity of drawing venn diagrams

Johnson, David S.; Pollak, H. O.

doi:10.1002/jgt.3190110306

Cited by 64 publications

(75 citation statements)

References 17 publications

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“…Planarity of (undirected) hypergraphs was studied by Johnson & Pollak (1987), on a paper that presents three approaches of planarity. The first one, based on Zycov planarity, is very convenient for the edge standard.…”

Section: Directed Hypergraph Planaritymentioning

confidence: 99%

“…Each vertex of V is represented by a vertex and each hyperedge is represented by a face of the planar map. Johnson & Pollak (1987) define Zykov planarity using a bipartite graph associated with the hypergraph (see also Walsh, 1975).…”

Section: Directed Hypergraph Planaritymentioning

confidence: 99%

“…Although graphs and digraphs are widely studied in graph drawing, the same cannot be said about directed hypergraphs. Planarity of hypergraphs was studied by Johnson & Pollak (1987) and their paper yields our theoretical approach. Mäkinen (1990) gives emphasis to the drawing of hypergraphs, where planarity plays an important role.…”

Section: Introductionmentioning

confidence: 99%

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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: Directed Hypergraph Planaritymentioning

confidence: 99%

Section: Directed Hypergraph Planaritymentioning

confidence: 99%

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Directed hypergraph planarity

Guedes

Markenzon

2005

Pesqui. Oper.

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“…Motivated by this fact, Pollak and Johnson [9] study alternative definitions of hypergraph planarity which are implied by yet two more methods to draw hypergraphshyperedge-based Venn diagrams and vertex-based Venn diagrams. (The choice of these In a hyperedge-based Venn diagram, hyperedges correspond uniquely to the faces of a planar subdivision in such a way that for any vertex v, the union of the faces corresponding to hyperedges that contain v, is connected.…”

Section: Introductionmentioning

confidence: 99%

“…We also show that there are hypergraphs which have a subdivision drawing, but not a simple subdivision drawing, and hypergraphs which have a simple, but not a compact subdivision drawing. Pollack and Johnson [9] proved that it is NP-complete to decide if a given hypergraph has a subdivision drawing. Nevertheless, there are classes of graphs that always have a subdivision drawing.…”

Section: Introductionmentioning

confidence: 99%

Subdivision Drawings of Hypergraphs

Kaufmann

Kreveld

Speckmann

2009

Lecture Notes in Computer Science

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Abstract. We introduce the concept of subdivision drawings of hypergraphs. In a subdivision drawing each vertex corresponds uniquely to a face of a planar subdivision and, for each hyperedge, the union of the faces corresponding to the vertices incident to that hyperedge is connected. Vertex-based Venn diagrams and concrete Euler diagrams are both subdivision drawings. In this paper we study two new types of subdivision drawings which are more general than concrete Euler diagrams and more restricted than vertex-based Venn diagrams. They allow us to draw more hypergraphs than the former while having better aesthetic properties than the latter.

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Drawing Hypergraphs in the Subset Standard (Short Demo Paper)

Bertault

Eades

2001

Lecture Notes in Computer Science

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Abstract.We report an experience on a practical system for drawing hypergraphs in the subset standard. The Patate system is based on the application of a classical force directed method to a dynamic graph, which is deduced, at a given iteration time, from the hypergraph structure and particular vertex locations. Different strategies to define the dynamic underlying graph are presented. We illustrate in particular the method when the graph is obtained by computing an Euclidean Steiner tree.

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Hypergraph planarity and the complexity of drawing venn diagrams

Cited by 64 publications

References 17 publications

Directed hypergraph planarity

Directed hypergraph planarity

Subdivision Drawings of Hypergraphs

Drawing Hypergraphs in the Subset Standard (Short Demo Paper)

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