Mad at Edge Crossings? Break the Edges!

Bruckdorfer, Till; Kaufmann, Michael

doi:10.1007/978-3-642-30347-0_7

Cited by 21 publications

(19 citation statements)

References 12 publications

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“…In this section, we improve, for specific graph classes, the result of Bruckdorfer and Kaufmann [5] which says that K n (and thus, any n-vertex graph) has a 1/ 4n/π-SHPED. In other words, K n has a δ-SHPED if n ≤ π/(4δ 2 ).…”

Section: Improved Bounds For Specific Graph Classesmentioning

confidence: 86%

“…Bruckdorfer and Kaufmann [5] gave an integer-linear program for MAXSPED and conjectured that the problem is NP-hard. Indeed, there is a simple reduction from PLA-NAR3SAT [13].…”

Section: Geometrically Embedded Spedsmentioning

confidence: 99%

“…We build on and extend the work of Bruckdorfer and Kaufmann [5] who formalized the problem of partial edge drawings (PEDs) and suggested several variants. A PED is a straight-line drawing of a graph in which each edge is divided into three segments: a middle part that is not drawn and the two segments incident to the vertices, called stubs, that remain in the drawing.…”

Section: Introductionmentioning

confidence: 99%

“…Our proof technique carries over to other values of the stub-edge length ratio δ. -Recall that Bruckdorfer and Kaufmann [5] showed that K n (and thus, any n-vertex graph) has a 1/ 4n/π-SHPED. We improve their result for specific graph classes, namely for complete bipartite graphs and for bandwidth-k graphs; see Sect.…”

Section: Introductionmentioning

confidence: 99%

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Progress on Partial Edge Drawings

et al. 2013

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Abstract. Recently, a new way of avoiding crossings in straight-line drawings of non-planar graphs has been investigated. The idea of partial edge drawings (PED) is to drop the middle part of edges and rely on the remaining edge parts called stubs. We focus on a symmetric model (SPED) that requires the two stubs of an edge to be of equal length. In this way, the stub at the other endpoint of an edge assures the viewer of the edge's existence. We also consider an additional homogeneity constraint that forces the stub lengths to be a given fraction δ of the edge lengths (δ-SHPED). Given length and direction of a stub, this model helps to infer the position of the opposite stub.We show that, for a fixed stub-edge length ratio δ, not all graphs have a δ-SHPED. Specifically, we show that K241 does not have a 1/4-SHPED, while bandwidth-k graphs always have a Θ(1/ √ k)-SHPED. We also give bounds for complete bipartite graphs. Further, we consider the problem MAXSPED where the task is to compute the SPED of maximum total stub length that a given straight-line drawing contains. We present an efficient solution for 2-planar drawings and a 2-approximation algorithm for the dual problem.

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Section: Improved Bounds For Specific Graph Classesmentioning

confidence: 86%

“…Bruckdorfer and Kaufmann [5] gave an integer-linear program for MAXSPED and conjectured that the problem is NP-hard. Indeed, there is a simple reduction from PLA-NAR3SAT [13].…”

Section: Geometrically Embedded Spedsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Progress on Partial Edge Drawings

et al. 2013

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“…User studies have confirmed that such drawings remain readable while reducing clutter significantly [9,12] and Burch et al [11] presented an interactive graph visualization tool using partially drawn edges combined with fully drawn edges. The idea of drawing edges only partially has subsequently been formalized in graph drawing as follows [7]. A partial edge drawing (PED) is a graph drawing that maps vertices to points and edges to pairs of crossing-free edge stubs of positive length pointing towards each other.…”

Section: Introductionmentioning

confidence: 99%

Maximizing Ink in Partial Edge Drawings of k-plane Graphs

Hummel

Klute

Nickel

et al. 2019

Lecture Notes in Computer Science

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Partial edge drawing (PED) is a drawing style for non-planar graphs, in which edges are drawn only partially as pairs of opposing stubs on the respective end-vertices. In a PED, by erasing the central parts of edges, all edge crossings and the resulting visual clutter are hidden in the undrawn parts of the edges. In symmetric partial edge drawings (SPEDs), the two stubs of each edge are required to have the same length. It is known that maximizing the ink (or the total stub length) when transforming a straight-line graph drawing with crossings into a SPED is tractable for 2-plane input drawings, but NP-hard for unrestricted inputs. We show that the problem remains NP-hard even for 3-plane input drawings and establish NP-hardness of ink maximization for PEDs of 4-plane graphs. Yet, for k-plane input drawings whose edge intersection graph forms a collection of trees or, more generally, whose intersection graph has bounded treewidth, we present efficient algorithms for computing maximum-ink PEDs and SPEDs. We implemented the treewidth-based algorithms and show a brief experimental evaluation.

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Perception of Symmetries in Drawings of Graphs

Luca

Kobourov

Purchase

2018

Lecture Notes in Computer Science

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Symmetry is an important factor in human perception in general, as well as in the visualization of graphs in particular. There are three main types of symmetry: reflective, translational, and rotational. We report the results of a human subjects experiment to determine what types of symmetries are more salient in drawings of graphs. We found statistically significant evidence that vertical reflective symmetry is the most dominant (when selecting among vertical reflective, horizontal reflective, and translational). We also found statistically significant evidence that rotational symmetry is affected by the number of radial axes (the more, the better), with a notable exception at four axes.

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Mad at Edge Crossings? Break the Edges!

Cited by 21 publications

References 12 publications

Progress on Partial Edge Drawings

Progress on Partial Edge Drawings

Maximizing Ink in Partial Edge Drawings of k-plane Graphs

Perception of Symmetries in Drawings of Graphs

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