Experimental Evaluation of Book Drawing Algorithms

Klawitter, Jonathan; Mchedlidze, Tamara; Nöllenburg, Martin

doi:10.1007/978-3-319-73915-1_19

Cited by 10 publications

(8 citation statements)

References 34 publications

(62 reference statements)

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“…The process is repeated x times, for a random number x ∈ [0.3n, 0.4n]. In contrast to the experimental work on crossing minimization in book embeddings [16], we did not observe that our heuristic performs differently on the topological and geometric 1-Planar graphs, see Appendix A . Hence, we merge the two classes into a single class.…”

Section: Northmentioning

confidence: 68%

A Greedy Heuristic for Crossing-Angle Maximization

Demel

Dürrschnabel

Mchedlidze

et al. 2018

Lecture Notes in Computer Science

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The crossing angle of a straight-line drawing Γ of a graph G = (V, E) is the smallest angle between two crossing edges in Γ . Deciding whether a graph G has a straight-line drawing with a crossing angle of 90 • is N P-hard [1]. We propose a simple heuristic to compute a drawing with a large crossing angle. The heuristic greedily selects the best position for a single vertex in a random set of points. The algorithm is accompanied by a speed-up technique to compute the crossing angle of a straight-line drawing. We show the effectiveness of the heuristic in an extensive empirical evaluation. Our heuristic was clearly the winning algorithm (CoffeeVM) in the Graph Drawing Challenge 2017 [6].

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Section: Northmentioning

confidence: 68%

A Greedy Heuristic for Crossing-Angle Maximization

Demel

Dürrschnabel

Mchedlidze

et al. 2018

Lecture Notes in Computer Science

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“…For other graphs, the vertex order has a strong effect on the results. In our experiments we first compared three state-of-the-art vertex order heuristics (breadth-first search (rbfs [13]), depth-first search (AVSDF [7]) and connectivity (conGreedy [10])) before applying the page assignment heuristics. It turned out that for all of them the same vertex order heuristic performed best on the same graph class, so that all experiments could be run without bias on exactly the same input order.…”

Section: Methodsmentioning

confidence: 99%

“…Most heuristics for minimizing crossings in book drawings work in two steps [10]. First compute a vertex order and then a page assignment.…”

Section: Heuristic Algorithmmentioning

confidence: 99%

“…Due to their practical relevance, book drawings, i.e., stack layouts in which crossings are allowed, have also been investigated from a practical point of view. Klawitter et al [10] surveyed the literature and performed an experimental study on several stateof-the-art book drawing algorithms aiming to minimize the number of crossings in layouts on a fixed number of stack pages. Conversely, for queue layouts it was a longstanding open question whether planar graphs have bounded queue number [8]; this was recently answered positively by Dujmović et al [4].…”

Section: Introductionmentioning

confidence: 99%

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Mixed Linear Layouts: Complexity, Heuristics, and Experiments

Col

Klute

Nöllenburg

2019

Lecture Notes in Computer Science

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A k-page linear graph layout of a graph G = (V, E) draws all vertices along a line and each edge in one of k disjoint halfplanes called pages, which are bounded by . We consider two types of pages. In a stack page no two edges should cross and in a queue page no edge should be nested by another edge. A crossing (nesting) in a stack (queue) page is called a conflict. The algorithmic problem is twofold and requires to compute (i) a vertex ordering and (ii) a page assignment of the edges such that the resulting layout is either conflict-free or conflict-minimal. While linear layouts with only stack or only queue pages are well-studied, mixed s-stack q-queue layouts for s, q ≥ 1 have received less attention. We show NP-completeness results on the recognition problem of certain mixed linear layouts and present a new heuristic for minimizing conflicts. In a computational experiment for the case s, q = 1 we show that the new heuristic is an improvement over previous heuristics for linear layouts.

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“…38 Several papers also study edge crossings and crossing minimization in arc-diagrams. 39−43 Applications of arc diagrams to the visualization of directed graphs have also been proposed. 44 We finally remark that arc diagrams are conceptually related to circular drawings and chord diagrams , where the vertices are placed on a circle and the edges are lines that can be embedded inside or outside this circle.…”

Section: Models Metrics and Algorithmsmentioning

confidence: 99%

Stable visualization of connected components in dynamic graphs

Giacomo

Didimo

Kaufmann

et al. 2020

Information Visualization

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One of the primary goals of many systems for the visual analysis of dynamically changing networks is to maintain the stability of the drawing throughout the sequence of graph changes. We investigate the scenario where the changes are determined by a stream of events, each being either an edge addition or an edge removal. The visualization must be updated immediately after each new event is received. Our main goal is to provide the user with an intuitive visualization that highlights the different connected components of the graph while preserving the user’s mental map after each event. The drawing stability is measured in terms of changes in the orthogonal relationships between vertices of two consecutive drawings. We describe two different visualization models, one for the 1-dimensional space and the other for the 2-dimensional space. In both models the connected components are drawn inside rectangular regions. To validate our approach, we report the results of an experimental analysis that compares the drawing stability of the online algorithm with that of an offline algorithm that knows in advance the whole sequence of events. We also present a case study of our online algorithm on a collaboration network.

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Experimental Evaluation of Book Drawing Algorithms

Cited by 10 publications

References 34 publications

A Greedy Heuristic for Crossing-Angle Maximization

A Greedy Heuristic for Crossing-Angle Maximization

Mixed Linear Layouts: Complexity, Heuristics, and Experiments

Stable visualization of connected components in dynamic graphs

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