On Computing Optimal Linear Diagrams

Alexander, Dobler,; Nöllenburg, Martin

doi:10.1007/978-3-031-15146-0_2

Cited by 2 publications

(4 citation statements)

References 28 publications

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“…Additionally, we show in the supplementary material [DN23] that planar temporal treemaps – those which have a layout with zero crossings ‐ can be recognized in polynomial time.…”

Section: Algorithms For Minimizing Crossingsmentioning

confidence: 99%

“…M edi computed the layout in only 20ms, and has half the crossings of KW but still 8 times more than ILP. More examples are in the supplementary material [DN23].…”

Section: Application Examplementioning

confidence: 99%

“…We define two associated computational problems of minimizing the two types of crossings. In Section 5.1 we show that both problems are generally NP‐hard. In the supplementary material [DN23] we give polynomial algorithms that determine if a solution with zero crossings exists. In Section 5.2 we discuss the algorithms by Köpp and Weinkauf [KW19] in more detail. We observe some drawbacks in those algorithms that we want to circumvent in our algorithms. In Section 5.3 we give exact algorithms that compute optimal solutions with the minimum number of crossings. In Section 5.4 we give a set of new heuristic algorithms. In Section 6 we conduct an experimental evaluation of the existing and new algorithms. Finally, in Section 7, we showcase the effect of more rigorous crossing minimization in an example for a real‐world dataset.…”

Section: Introductionmentioning

confidence: 99%

“…The implementations of algorithms in this paper make use of the code‐base of Köpp and Weinkauf [KW19]. All implementations, datasets, additional experimental evaluations, and additional examples of temporal treemaps are available on OSF [DN23].…”

Section: Introductionmentioning

confidence: 99%

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Improving Temporal Treemaps by Minimizing Crossings

Dobler,

Nöllenburg

2024

Computer Graphics Forum

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Temporal trees are trees that evolve over a discrete set of time steps. Each time step is associated with a node‐weighted rooted tree and consecutive trees change by adding new nodes, removing nodes, splitting nodes, merging nodes, and changing node weights. Recently, two‐dimensional visualizations of temporal trees called temporal treemaps have been proposed, representing the temporal dimension on the x‐axis, and visualizing the tree modifications over time as temporal edges of varying thickness. The tree hierarchy at each time step is depicted as a vertical, one‐dimensional nesting relationships, similarly to standard, non‐temporal treemaps. Naturally, temporal edges can cross in the visualization, decreasing readability. Heuristics were proposed to minimize such crossings in the literature, but a formal characterization and minimization of crossings in temporal treemaps was left open. In this paper, we propose two variants of defining crossings in temporal treemaps that can be combinatorially characterized. For each variant, we propose an exact optimization algorithm based on integer linear programming and heuristics based on graph drawing techniques. In an extensive experimental evaluation, we show that on the one hand the exact algorithms reduce the number of crossings by a factor of 20 on average compared to the previous algorithms. On the other hand, our new heuristics are faster by a factor of more than 100 and still reduce the number of crossings by a factor of almost three.

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“…Additionally, we show in the supplementary material [DN23] that planar temporal treemaps – those which have a layout with zero crossings ‐ can be recognized in polynomial time.…”

Section: Algorithms For Minimizing Crossingsmentioning

confidence: 99%

“…M edi computed the layout in only 20ms, and has half the crossings of KW but still 8 times more than ILP. More examples are in the supplementary material [DN23].…”

Section: Application Examplementioning

confidence: 99%