Mixed Linear Layouts: Complexity, Heuristics, and Experiments

Col, Philipp de; Klute, Fabian; Nöllenburg, Martin

doi:10.1007/978-3-030-35802-0_35

Cited by 12 publications

(4 citation statements)

References 14 publications

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“…This is mostly the case for papers that distribute their dataset as supplemental material. In some cases, too, there is no ambiguity in how the graphs are generated, such as when authors use complete graphs of increasing sizes [CIW21b,CHN19,dCKN19]. In our survey we found 68 papers using custom datasets, 25% being replicable, 26.5% being reproducible, while the rest (48.5%) was non-replicable.…”

Section: Generatedmentioning

confidence: 90%

Evaluating Graph Layout Algorithms: A Systematic Review of Methods and Best Practices

Bartolomeo¹,

Crnovrsanin²,

Saffo³

et al. 2023

Preprint

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Computational evaluations and benchmarks are widely used for validating graph and network layout algorithms (a.k.a. graph drawing). These evaluations can provide the reader with substantial insight into the performance and capabilities of the algorithm. Moreover, computational evaluations can help the reader determine whether the algorithm would fit a specific purpose, for example, graphs with many nodes or dense graphs. There is no standard approach for evaluating layout algorithms. Prior work holds a ``Wild West'' of diverse benchmark datasets and data characteristics, as well as varied evaluation metrics and ways to report results. It is often difficult to compare layout algorithms without first implementing them and then running your own evaluation. In this systematic review of past research, we examine the various methods used to run computational evaluations, the techniques used, the results reported, and the advantages and disadvantages of using one methodology over another. The proposed systematic review---and accompanying website---will guide readers through evaluation types, the types of results reported, and the available benchmark datasets and their data characteristics.

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Section: Generatedmentioning

confidence: 90%

Evaluating Graph Layout Algorithms: A Systematic Review of Methods and Best Practices

Bartolomeo¹,

Crnovrsanin²,

Saffo³

et al. 2023

Preprint

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“…3. Finally, we mention the possibility of studying the parameterized complexity of mixed linear layouts, using both queues and stacks, see [6,16,21,25].…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Parameterized Algorithms for Book Embedding Problems

Bhore¹,

Ganian²,

Montecchiani³

et al. 2020

JGAA

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A k-page book embedding of a graph G draws the vertices of G on a line and the edges on k half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether G admits a k-page book embedding both when the linear order of the vertices is fixed, called Fixed-Order Book Thickness, or not fixed, called Book Thickness. Both problems are known to be NP-complete in general. We show that Fixed-Order Book Thickness and Book Thickness are fixed-parameter tractable parameterized by the vertex cover number of the graph and that Fixed-Order Book Thickness is fixed-parameter tractable parameterized by the pathwidth of the vertex order.

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“…We conclude with an algorithmic question, namely, what is the complexity of recognizing graphs that admit mixed 1-stack 1-queue layouts, even for 2-trees? Note that recently de Col et al [9] showed that testing whether a (not necessarily planar) graph admits a mixed 2-stack 1-queue layout is NP-complete.…”

Section: Open Problemsmentioning

confidence: 99%

On Mixed Linear Layouts of Series-Parallel Graphs

Angelini¹,

Bekos²,

Kindermann³

et al. 2020

Preprint

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A mixed s-stack q-queue layout of a graph consists of a linear order of its vertices and of a partition of its edges into s stacks and q queues, such that no two edges in the same stack cross and no two edges in the same queue nest. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed 1-stack 1-queue layout. Recently, Pupyrev disproved this conjectured by demonstrating a planar partial 3-tree that does not admit a 1-stack 1-queue layout. In this note, we strengthen Pupyrev's result by showing that the conjecture does not hold even for 2-trees, also known as series-parallel graphs.

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Mixed Linear Layouts: Complexity, Heuristics, and Experiments

Cited by 12 publications

References 14 publications

Evaluating Graph Layout Algorithms: A Systematic Review of Methods and Best Practices

Evaluating Graph Layout Algorithms: A Systematic Review of Methods and Best Practices

Parameterized Algorithms for Book Embedding Problems

On Mixed Linear Layouts of Series-Parallel Graphs

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