A Heuristic Approach Towards Drawings of Graphs With High Crossing Resolution

Bekos, Michael A.; Förster, Henry; Geckeler, Christian; Holländer, Lukas; Kaufmann, Michael; Spallek, Amadäus M.; Splett, Jan

doi:10.1093/comjnl/bxz133

Cited by 7 publications

(12 citation statements)

References 36 publications

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“…Formally, the crossing angle of a straight-line drawing of a graph is the minimum angle between two crossing edges in the layout, and optimizing this property is also NP-hard. Recent graph drawing contests have been organized with the objective of maximizing the crossings angle in graph drawings and this has led to several heuristics for this problem [6], [16].…”

Section: Related Workmentioning

confidence: 99%

“…When edge crossings are unavoidable, the graph drawing can still be easier to read when edges cross at angles close to 90 degrees [55]. Heuristics such as those by Demel et al [16] and Bekos et al [6] have been proposed and have been successful in graph drawing challenges [17]. We use an approach similar to the force-directed algorithm given by Eades et al [26] and minimize the squared cosine of crossing angles:…”

Section: Crossing Angle Maximizationmentioning

confidence: 99%

See 1 more Smart Citation

Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, $(SGD)^2$

Ahmed¹,

Luca²,

Devkota³

et al. 2021

Preprint

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Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically optimize one such criterion, usually at the expense of others. We propose a layout approach, Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, (SGD) 2 , that can handle multiple readability criteria. (SGD) 2 can optimize any criterion that can be described by a differentiable function. Our approach is flexible and can be used to optimize several criteria that have already been considered earlier (e.g., obtaining ideal edge lengths, stress, neighborhood preservation) as well as other criteria which have not yet been explicitly optimized in such fashion (e.g., node resolution, angular resolution, aspect ratio). The approach is scalable and can handle large graphs. A variation of the underlying approach can also be used to optimize many desirable properties in planar graphs, while maintaining planarity. Finally, we provide quantitative and qualitative evidence of the effectiveness of (SGD) 2 : we analyze the interactions between criteria, measure the quality of layouts generated from (SGD) 2 as well as the runtime behavior, and analyze the impact of sample sizes. The source code is available on github and we also provide an interactive demo for small graphs.

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Section: Related Workmentioning

confidence: 99%

Section: Crossing Angle Maximizationmentioning

confidence: 99%

Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, $(SGD)^2$

Ahmed¹,

Luca²,

Devkota³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

Section: Related Workmentioning

confidence: 99%

“…When edge crossings are unavoidable, the graph drawing can still be easier to read when edges cross at angles close to 90 degrees [36]. Heuristics such as those by Demel et al [11] and Bekos et al [4] have been proposed and have been successful in graph drawing challenges [12]. We use an approach similar to the force-directed algorithm given by Eades et al [19] and minimize the squared cosine of crossing angles:…”

Section: Crossing Angle Maximizationmentioning

confidence: 99%

Graph Drawing via Gradient Descent, $(GD)^2$

Ahmed

Luca

Devkota

et al. 2020

Preprint

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Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically optimize one such criterion, usually at the expense of others. We propose a layout approach, Graph Drawing via Gradient Descent, (GD) 2 , that can handle multiple readability criteria. (GD) 2 can optimize any criterion that can be described by a smooth function. If the criterion cannot be captured by a smooth function, a non-smooth function for the criterion is combined with another smooth function, or auto-differentiation tools are used for the optimization. Our approach is flexible and can be used to optimize several criteria that have already been considered earlier (e.g., obtaining ideal edge lengths, stress, neighborhood preservation) as well as other criteria which have not yet been explicitly optimized in such fashion (e.g., vertex resolution, angular resolution, aspect ratio). We provide quantitative and qualitative evidence of the effectiveness of (GD) 2 with experimental data and a functional prototype: http://hdc.cs.arizona.edu/ ~mwli/graph-drawing/.

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“…They presented drawings of complete and complete bipartite graphs with asymptotically optimal total angular resolution. Recently Bekos et al [4] presented a new algorithm for finding a drawing of a given graph with high total angular resolution which was performing superior to earlier algorithms like [3,9] on the considered test cases.…”

Section: Introductionmentioning

confidence: 99%

Graphs with Large Total Angular Resolution

Aichholzer

Korman

Okamoto

et al. 2019

Lecture Notes in Computer Science

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0000−0002−2364−0583] , Matias Korman 2 , Yoshio Okamoto 3[0000−0002−9826−7074] , Irene Parada 1[0000−0003−3147−0083] , Daniel Perz 1[0000−0002−6557−2355] , André van Renssen 4[0000−0002−9294−9947] , and Birgit Vogtenhuber 1[0000−0002−7166−4467]Abstract. The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove that, up to a finite number of well specified exceptions of constant size, the number of edges of a graph with n vertices and a total angular resolution greater than 60 • is bounded by 2n − 6. This bound is tight. In addition, we show that deciding whether a graph has total angular resolution at least 60 • is NP-hard.

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A Heuristic Approach Towards Drawings of Graphs With High Crossing Resolution

Cited by 7 publications

References 36 publications

Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, $(SGD)^2$

Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, $(SGD)^2$

Graph Drawing via Gradient Descent, $(GD)^2$

Graphs with Large Total Angular Resolution

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