Simultaneous Orthogonal Planarity

Angelini, Patrizio; Chaplick, Steven; Cornelsen, Sabine; Lozzo, Giordano Da; Battista, Giuseppe Di; Eades, Peter; Kindermann, Philipp; Kratochvíl, Jan; Lipp, Fabian; Rutter, Ignaz

doi:10.1007/978-3-319-50106-2_41

Cited by 9 publications

(6 citation statements)

References 32 publications

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“…We now show that to solve an instance (G, H, Γ H ) of the RepExt(ortho) problem, it suffices to only consider the port constraints determined by Γ H together with the embedding E H of H in Γ H . More specifically, we prove the following characterization, which could also be deduced from [1].…”

Section: Preliminariesmentioning

confidence: 65%

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Extending Partial Orthogonal Drawings

Angelini¹,

Rutter²,

Sandhya³

2021

JGAA

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We study the planar orthogonal drawing style within the framework of partial representation extension. Let (G, H, ΓH ) be a partial orthogonal drawing, i.e., G is a graph, H ⊆ G is a subgraph and ΓH is a planar orthogonal drawing of H. We show that the existence of an orthogonal drawing ΓG of G that extends ΓH can be tested in linear time. If such a drawing exists, then there also is one that uses O(|V (H)|) bends per edge. On the other hand, we show that it is NP-complete to find an extension that minimizes the number of bends or has a fixed number of bends per edge.

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Section: Preliminariesmentioning

confidence: 65%

“…In light of this popularity and the existence of a strongly developed theory, it is surprising that the planar orthogonal drawings have not been investigated within the framework of partial representation extension. Especially so, since it has been considered in the related context of simultaneous representations [1].…”

Section: Introductionmentioning

confidence: 99%

Extending Partial Orthogonal Drawings

Angelini¹,

Rutter²,

Sandhya³

2021

JGAA

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“…We refer the reader to [6] for an older literature overview. The problem has been considered for orthogonal drawings [2] and level-planar drawings [3]. Up to our knowledge, neither partial nor simultaneous drawings have been considered in the restricted slope setting.…”

Section: Related Workmentioning

confidence: 99%

Level-Planar Drawings with Few Slopes

2021

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We introduce and study level-planar straight-line drawings with a fixed number $$\lambda $$ λ of slopes. For proper level graphs (all edges connect vertices of adjacent levels), we give an $$O(n \log ^2 n / \log \log n)$$ O ( n log 2 n / log log n ) -time algorithm that either finds such a drawing or determines that no such drawing exists. Moreover, we consider the partial drawing extension problem, where we seek to extend an immutable drawing of a subgraph to a drawing of the whole graph, and the simultaneous drawing problem, which asks about the existence of drawings of two graphs whose restrictions to their shared subgraph coincide. We present $$O(n^{4/3} \log n)$$ O ( n 4 / 3 log n ) -time and $$O(\lambda n^{10/3} \log n)$$ O ( λ n 10 / 3 log n ) -time algorithms for these respective problems on proper level-planar graphs. We complement these positive results by showing that testing whether non-proper level graphs admit level-planar drawings with $$\lambda $$ λ slopes is -hard even in restricted cases.

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“…So, in some sense, our problem seems to be more related to nearly-planar simultaneous embeddings, where the input graphs are allowed to cross, as long as they avoid some local crossing configurations, e.g., by avoiding triples of mutually crossing edges [16]. Note that the Sefe problem has also been studied in several settings [2,6,12,17]. An interpretation of Partial Planarity, which also extends to Hierarchical Partial Planarity, in terms of a special version of Sefe, called Sunflower Sefe [8], was already observed in [1].…”

Section: Problem Formulation and Relationships To Other Problemsmentioning

confidence: 99%

Hierarchical Partial Planarity

Angelini

Bekos

2018

Algorithmica

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In this paper we consider graphs whose edges are associated with a degree of importance, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to construct layouts of these graphs in which the readability of an edge is proportional to its importance, that is, more important edges have fewer crossings. We formalize this problem and study the case in which there exist three different degrees of importance. We give a polynomial-time testing algorithm when the graph induced by the two most important sets of edges is biconnected. We also discuss interesting relationships with other constrained-planarity problems.

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Simultaneous Orthogonal Planarity

Cited by 9 publications

References 32 publications

Extending Partial Orthogonal Drawings

Extending Partial Orthogonal Drawings

Level-Planar Drawings with Few Slopes

Hierarchical Partial Planarity

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