Short Plane Supports for Spatial Hypergraphs

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CASTERMANS, Thom, Mereke VAN GARDEREN, Wouter MEULEMANS, Martin NÖLLENBURG, Xiaoru YUAN, 2019. Short Plane Supports for Spatial Hypergraphs. In: Journal of Graph Algorithms and Applications. European Mathematical Society (EMS). 23(3), pp. 463-498. eISSN 1526-1719. Available under: doi: 10.7155/jgaa.00499

@article{Castermans2019Short-57309, title={Short Plane Supports for Spatial Hypergraphs}, year={2019}, doi={10.7155/jgaa.00499}, number={3}, volume={23}, journal={Journal of Graph Algorithms and Applications}, pages={463--498}, author={Castermans, Thom and van Garderen, Mereke and Meulemans, Wouter and Nöllenburg, Martin and Yuan, Xiaoru} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:hasPart rdf:resource=""/> <dspace:isPartOfCollection rdf:resource=""/> <dcterms:rights rdf:resource=""/> <dcterms:title>Short Plane Supports for Spatial Hypergraphs</dcterms:title> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:available rdf:datatype="">2022-04-19T16:30:33Z</dcterms:available> <dc:language>eng</dc:language> <dc:rights>terms-of-use</dc:rights> <dc:contributor>Yuan, Xiaoru</dc:contributor> <dc:creator>Meulemans, Wouter</dc:creator> <dc:date rdf:datatype="">2022-04-19T16:30:33Z</dc:date> <dc:contributor>van Garderen, Mereke</dc:contributor> <dcterms:isPartOf rdf:resource=""/> <dc:creator>Yuan, Xiaoru</dc:creator> <dcterms:abstract xml:lang="eng">A graph G = (V;E) is a support of a hypergraph H = (V; S) if every hyperedge induces a connected subgraph in G. Supports are used for cer- tain types of hypergraph drawings, also known as set visualizations. In this paper we consider visualizing spatial hypergraphs, where each ver- tex has a fixed location in the plane. This scenario appears when, e.g., modeling set systems of geospatial locations as hypergraphs. Following established aesthetic quality criteria, we are interested in finding supports that yield plane straight-line drawings with minimum total edge length on the input point set V . From a theoretical point of view, we first show that the problem is NP-hard already under rather mild conditions, and additionally provide a negative approximability result. Therefore, the main focus of the paper lies on practical heuristic algorithms as well as an exact, ILP-based approach for computing short plane supports. We report results from computational experiments that investigate the effect of requiring planarity and acyclicity on the resulting support length. Fur- thermore, we evaluate the performance and trade-offs between solution quality and speed of heuristics relative to each other and compared to optimal solutions.</dcterms:abstract> <dc:contributor>Meulemans, Wouter</dc:contributor> <bibo:uri rdf:resource=""/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:contributor>Castermans, Thom</dc:contributor> <dspace:hasBitstream rdf:resource=""/> <dc:creator>Nöllenburg, Martin</dc:creator> <dc:creator>Castermans, Thom</dc:creator> <dcterms:issued>2019</dcterms:issued> <dc:contributor>Nöllenburg, Martin</dc:contributor> <dc:creator>van Garderen, Mereke</dc:creator> </rdf:Description> </rdf:RDF>

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