Subdivision Drawings of Hypergraphs

Kaufmann, Michael; Kreveld, Marc van; Speckmann, Bettina

doi:10.1007/978-3-642-00219-9_39

Cited by 44 publications

(43 citation statements)

References 15 publications

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“…Then a Kelp Diagram is a realization of a hypergraph support, as discussed by Kaufmann et al [12], Buchin et al [5], and Brandes et al [3]. Though the concepts explored in these papers consider structures similar to Kelp Diagrams and LineSets, they are more concerned with their graph theoretical properties, such as existence theorems for various classes of supports, than with application to practical visualization.…”

Section: Related Workmentioning

confidence: 99%

KelpFusion: A Hybrid Set Visualization Technique

Meulemans

Riche

Speckmann

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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102

101

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• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract-We present KelpFusion: a method for depicting set membership of items on a map or other visualization using continuous boundaries. KelpFusion is a hybrid representation that bridges hull techniques such as Bubble Sets and Euler Diagrams and line-and graph-based techniques such as LineSets and Kelp Diagrams. We describe an algorithm based on shortest-path graphs to compute KelpFusion visualizations. Based on a single parameter, the shortest-path graph varies from the minimal spanning tree to the convex hull of a point set. Shortest-path graphs aim to capture the shape of a point set and smoothly adapt to sets of varying densities. KelpFusion fills enclosed faces based on a set of simple legibility rules. We present the results of a controlled experiment comparing KelpFusion to Bubble Sets and LineSets. We conclude that KelpFusion outperforms Bubble Sets both in accuracy and completion time, and outperforms LineSets in completion time.

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Section: Related Workmentioning

confidence: 99%

KelpFusion: A Hybrid Set Visualization Technique

Meulemans

Riche

Speckmann

et al. 2013

IEEE Trans. Visual. Comput. Graphics

Self Cite

102

101

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“…See the introductions of Kaufmann et al (2009) or Verroust-Blondet and Viaud (2004) for surveys on those drawings. Among those definitions, we consider two: the vertex-planarity by Johnson and Pollak (1987) and the planarity defined by Zykov (or Zykov-planarity).…”

Section: Planarity On Hypergraphsmentioning

confidence: 99%

Trinque problem: covering complete graphs by plane degree-bounded hypergraphs

2015

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“…Drawings of hypergraphs have been discussed in several papers, for example, by Kaufmann et al [21], Buchin et al [10], and Brandes et al [8].…”

Section: Introductionmentioning

confidence: 99%

Colored Spanning Graphs for Set Visualization

Hurtado

Korman

Kreveld

et al. 2013

Lecture Notes in Computer Science

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Abstract. We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected. We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem can be solved in polynomial time using matroid techniques. In addition, we discuss more efficient algorithms for the case in which points are located on a line or a circle, and also describe a fast ( 1 2 ρ + 1)-approximation algorithm, where ρ is the Steiner ratio.In memoriam : Ferran Hurtado (1951-2014 This paper was initiated during a research visit hosted by Ferran and his group in Barcelona. Following tradition, hours of research were complemented by relaxing evenings with great food and wine. The authors would like to thank Ferran for being a supportive mentor, an inspiring colleague, and a great friend.

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Subdivision Drawings of Hypergraphs

Cited by 44 publications

References 15 publications

KelpFusion: A Hybrid Set Visualization Technique

KelpFusion: A Hybrid Set Visualization Technique

Trinque problem: covering complete graphs by plane degree-bounded hypergraphs

Colored Spanning Graphs for Set Visualization

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