Upward Planarization Layout

Chimani, Markus; Gutwenger, Carsten; Mutzel, Petra; Wong, Hoi-Ming

doi:10.1007/978-3-642-11805-0_11

Cited by 10 publications

(13 citation statements)

References 20 publications

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“…The upward planarization layout (UPL) algorithm was a binary C ++ executable (provided by the authors of [Chimani et al 2011]) and the other algorithms were implemented in JAVA within Gravisto [Bachmaier et al 2004]. All tests in sum needed a (sequential) computation time of roughly 219 days.…”

Section: Resultsmentioning

confidence: 99%

“…Similarly to Chimani et al [2011], we apply a postprocessing step to reduce the number of levels without changing the crossing number. In the level embedding, we search for distinct (nonnecessarily monotonic) cuts from the left to the right which consist solely of dummy vertices (at most one of each edge block) and do not cross outer segments.…”

Section: Vertical Compactionmentioning

confidence: 99%

“…This time we fixed the number of vertices of each graph to 100, following the style of benchmarks for random graphs of Chimani et al [2011]. We drew 10 instances each from all connected DAGs with an exact density of d = |E| 100 ∈ {1.5, 1.6, .…”

Section: Synthetic Benchmarksmentioning

confidence: 99%

“…As a side effect, φ also imposes an ascending topological ordering on the vertices. We compared the algorithms iterative one-sided 2-level barycenter (BC) [Kaufmann and Wagner 2001], global sifting (GlS) [Bachmaier et al 2011], upward planarization layout (UPL) [Chimani et al 2011], and our grid sifting algorithm with the level radii 3 (GrS3), 10 (GrS10) and unconfined (GrS*). GrS21 uses radius 21 but odd (i.e., new) levels only.…”

Section: Synthetic Benchmarksmentioning

confidence: 99%

“…Recently, Chimani et al [2010Chimani et al [ , 2011 presented a planarization approach to reduce the number of crossings. They compute a planar upward embedding of the graph by adding dummy vertices where two edges would cross.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Grid sifting

Bachmaier

Brunner

Gleißner

2012

ACM J. Exp. Algorithmics

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Directed graphs are commonly drawn by the Sugiyama algorithm where first vertices are placed on distinct hierarchical levels, and second vertices on the same level are permuted to reduce the overall number of crossings. Separating these two phases simplifies the algorithms but diminishes the quality of the result.We introduce a combined leveling and crossing reduction algorithm based on sifting, which prioritizes few crossings over few levels. It avoids type 2 conflicts, which are crossings of edges whose endpoints are dummy vertices. This helps straightening long edges spanning many levels. The obtained running time is roughly quadratic in the size of the input graph and independent of dummy vertices.

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Section: Resultsmentioning

confidence: 99%

Section: Vertical Compactionmentioning

confidence: 99%

Section: Synthetic Benchmarksmentioning

confidence: 99%

Section: Synthetic Benchmarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Grid sifting

Bachmaier

Brunner

Gleißner

2012

ACM J. Exp. Algorithmics

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Graph Drawing Contest Report

et al. 2010

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Crossing Minimization and Layouts of Directed Hypergraphs with Port Constraints

et al. 2011

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Many practical applications for drawing graphs are modeled by directed graphs with domain specific constraints. In this paper, we consider the problem of drawing directed hypergraphs with (and without) port constraints, which cover multiple real-world graph drawing applications like data flow diagrams and electric schematics. Most existing algorithms for drawing hypergraphs with port constraints are adaptions of the framework originally proposed by Sugiyama et al. in 1981 for simple directed graphs. Recently, a practical approach for upward crossing minimization of directed graphs based on the planarization method was proposed [7]. With respect to the number of arc crossings, it clearly outperforms prior (mostly layering-based) approaches. We show how to adopt this idea for hypergraphs with given port constraints, obtaining an upward-planar representation (UPR) of the input hypergraph where crossings are modeled by dummy nodes. Furthermore, we present the new problem of computing an orthogonal upward drawing with minimal number of crossings from such an UPR, and show that it can be solved efficiently by providing a simple method. Markus Chimani was funded by a Carl-Zeiss-Foundation juniorprofessorship. Hoi-Ming Wong was supported by the German Research Foundation (DFG), priority project (SPP) 1307 "Algorithm Engineering", subproject "Planarization Practices in Automatic Graph Drawing".

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Upward Planarization Layout

Cited by 10 publications

References 20 publications

Grid sifting

Grid sifting

Graph Drawing Contest Report

Crossing Minimization and Layouts of Directed Hypergraphs with Port Constraints

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