Computing Quasi-Upward Planar Drawings of Mixed Graphs

Binucci, Carla; Didimo, Walter

doi:10.1093/comjnl/bxv082

Cited by 8 publications

(6 citation statements)

References 46 publications

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“…The new region R is delimited from the right by the same y-monotone curve ρ R as the old region R; the new y-monotone curve λ R delimiting R from the left is composed of (v) and of the straight-line vertical segments connecting v b and v a with Q i−1 and Q i , respectively. The new region R satisfies Properties (i)-(iii); in particular, for every unprocessed vertex u, the new region R contains in its interior u b and u a , provided that 2 (v) and 7 (v) are sufficiently close to the y-monotone curve λ R delimiting the old region R, and contains in its interior q(u), given that q(v) is to the left of q(u), by the definition of T i . This concludes the proof of the claim.…”

Section: Claimmentioning

confidence: 99%

“…In an upward planar drawing of a directed graph no two edges cross and an edge directed from a vertex u to a vertex v is represented by a curve monotonically increasing in the y-direction from u to v; the latter property effectively conveys the information about the direction of the edges of the graph. The study of upward planar drawings is a most prolific topic in the theory of graph visualization [2,4,5,6,7,8,10,14,15,17,19,29]. Garg and Tamassia showed that deciding the existence of an upward planar drawing is an NP-complete problem [19].…”

Section: Introductionmentioning

confidence: 99%

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Extending Upward Planar Graph Drawings

Lozzo

Battista

Frati

2019

Lecture Notes in Computer Science

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In this paper we study the computational complexity of the Upward Planarity Extension problem, which takes in input an upward planar drawing ΓH of a subgraph H of a directed graph G and asks whether ΓH can be extended to an upward planar drawing of G. Our study fits into the line of research on the extensibility of partial representations, which has recently become a mainstream in Graph Drawing. We show the following results.-First, we prove that the Upward Planarity Extension problem is NP-complete, even if G has a prescribed upward embedding, the vertex set of H coincides with the one of G, and H contains no edge. -Second, we show that the Upward Planarity Extension problem can be solved in O(n log n) time if G is an n-vertex upward planar st-graph. This result improves upon a known O(n 2 )-time algorithm, which however applies to all n-vertex single-source upward planar graphs. -Finally, we show how to solve in polynomial time a surprisingly difficult version of the Upward Planarity Extension problem, in which G is a directed path or cycle with a prescribed upward embedding, H contains no edges, and no two vertices share the same y-coordinate in ΓH .that the drawing of G we seek has to respect a given upward embedding, i.e., a left-to-right order of the edges entering and exiting each vertex. Related problems. Level planar drawings are special upward planar drawings. Klemz and Rote studied the Ordered Level Planarity (OLP) problem [26], where a partial drawing of a level graph is given containing all the vertices and no edges. The problem asks for the existence of a level planar drawing of the graph extending the partial one. They show a tight border of tractability for the problem by proving NP-completeness even if no three vertices have the same y-coordinate and by providing a linear-time algorithm if no two vertices have the same y-coordinate. Brückner and Rutter studied the Partial Level Planarity (PLP) problem [9], that is, the extensibility of a partial drawing of a level graph, which might contain (not necessarily all) vertices and edges. Beside proving NP-completeness even for connected graphs, they provided a quadratic-time algorithm for single-source graphs.The NP-hardness of the Upward Planarity Testing problem [19] directly implies the NP-hardness of the UPE problem, as the former coincides with the special case of the latter in which the partial graph is the empty graph. Further, we have that any instance of the OLP problem in which no λ vertices have the same y-coordinate can be transformed in linear time into an equivalent instance of the UPE problem in which the partial graph contains all the vertices and no edges, and no λ vertices have the same y-coordinate in the partial drawing; moreover, a linear-time reduction can also be performed in the opposite direction. As a consequence of these reductions and of the cited results about the complexity of the OLP problem, we obtain that the UPE problem is NP-hard even if the partial graph contains all the vertices and no edges, and no three vertices s...

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Section: Claimmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extending Upward Planar Graph Drawings

Lozzo

Battista

Frati

2019

Lecture Notes in Computer Science

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“…5) and their implementations are integrated in software libraries and systems, like OGDF and the yFiles library. Alternative techniques have been described for dealing with mixed graphs [12,14], vertices of prescribed size, and orthogonal drawings with prescribed clusters of vertices (see [80]).…”

Section: Software Engineeringmentioning

confidence: 99%

10 Reasons to Get Interested in Graph Drawing

Binucci

Brandes

Dwyer

et al. 2019

Lecture Notes in Computer Science

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This is an invitation to the research area of graph drawing. It encompasses basic research such as graph theory, complexity theory, data structures, and graph algorithms as well as applied research such as software libraries, implementations, and applications. Application domains include areas within computer science (e. g., information visualization, software engineering, model-based design, automated cartography) as well as outside (e. g., molecular biology and the social sciences). A selection of results demonstrates the influence of graph drawing on other areas and vice versa.

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“…Possible optimization goals for the visualization of such graphs can be inspired by recent works on this topic (see, e.g. [BD16, BDP14, EKE03]). The results of our user study clearly indicate that the OOD style leads to more accurate user's responses on tasks of analysis involving path and cycle recognition, when compared to other classical drawing styles.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

A Visualization Framework and User Studies for Overloaded Orthogonal Drawings

Didimo

Kornaropoulos

Montecchiani

et al. 2017

Computer Graphics Forum

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Overloaded orthogonal drawing (OOD) is a recent graph visualization style specifically conceived for directed graphs. It merges the advantages of some popular drawing conventions like layered drawings and orthogonal drawings, and provides additional support for some common analysis tasks. We present a visualization framework called DAGView, which implements algorithms and graphical features for the OOD style. Besides the algorithm for acyclic digraphs, the DAGView framework implements extensions to visualize both digraphs with cycles and undirected graphs, with the additional possibility of taking into account user preferences and constraints. It also supports an interactive visualization of clustered digraphs, based on the use of strongly connected components. Moreover, we describe an experimental user study, aimed to investigate the usability of OOD within the DAGView framework. The results of our study suggest that OOD can be effectively exploited to perform some basic tasks of analysis in a faster and more accurate way when compared to other drawing styles for directed graphs.

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Computing Quasi-Upward Planar Drawings of Mixed Graphs

Cited by 8 publications

References 46 publications

Extending Upward Planar Graph Drawings

Extending Upward Planar Graph Drawings

10 Reasons to Get Interested in Graph Drawing

A Visualization Framework and User Studies for Overloaded Orthogonal Drawings

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