Straight-Line Rectangular Drawings of Clustered Graphs

Angelini, Patrizio; Frati, Fabrizio; Kaufmann, Michael

doi:10.1007/s00454-010-9302-z

Cited by 15 publications

(9 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Conversely, suppose that C(G , T ) is c-planar. Then, it admits a c-planar straight-line drawing in which μ 1 and μ 2 are represented by convex regions R(μ 1 ) and R(μ 2 ) (see [4,17]). Thus, R(μ 1 ) and R(μ 2 ) can be separated by a straight line l; by suitably rotating l and the Cartesian axes, we can assume that l is horizontal and every edge of G is y-monotone in , with R(μ 1 ) below R(μ 2 ).…”

Section: Reductionmentioning

confidence: 99%

Strip Planarity Testing for Embedded Planar Graphs

et al. 2016

Self Cite

View full text Add to dashboard Cite

In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph G(V, E) and a function γ : V → {1, 2, . . . , k} and asks whether a planar drawing of G exists such that each edge is represented by a curve that is monotone in the y-direction and, for any u, v ∈ V with γ (u) < γ (v), it holds that y(u) < y(v). The problem has strong relationships with some of the most deeply studied variants of the planarity testing problem, such as clustered planarity, upward planarity, and level planarity. Most notably, we provide a polynomial-time reduction from strip planarity testing to clustered planarity. We show that the strip planarity testing problem is polynomial-time solvable if G has a prescribed combinatorial embedding.

show abstract

Section: Reductionmentioning

confidence: 99%

Strip Planarity Testing for Embedded Planar Graphs

et al. 2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…Concerning drawings of c-planar clustered graphs, Eades et al [10] prove that every c-planar graph has a c-planar straight-line drawing where each cluster is drawn in a convex region. Angelini et al [5] strengthen this result by showing that every c-planar graph has a c-planar straight-line drawing in which every cluster is drawn in an axis-parallel rectangle. The result of Akitaya et al [2] implies that in O(n log n) time one can decide whether an abstract graph with a flat clustering has an embedding where each vertex lies in a prescribed topological disk and every edge is routed through a prescribed topological pipe.…”

Section: Introductionmentioning

confidence: 89%

Drawing Clustered Graphs on Disk Arrangements

Mchedlidze

Radermacher

Rutter

et al. 2018

WALCOM: Algorithms and Computation

View full text Add to dashboard Cite

Let G = (V, E) be a planar graph and let V be a partition of V . We refer to the graphs induced by the vertex sets in V as clusters. Let DC be an arrangement of disks with a bijection between the disks and the clusters. Akitaya et al. [2] give an algorithm to test whether (G, V) can be embedded onto DC with the additional constraint that edges are routed through a set of pipes between the disks. Based on such an embedding, we prove that every clustered graph and every disk arrangement without pipe-disk intersections has a planar straight-line drawing where every vertex is embedded in the disk corresponding to its cluster. This result can be seen as an extension of the result by Alam et al. [3] who solely consider biconnected clusters. Moreover, we prove that it is N P-hard to decide whether a clustered graph has such a straight-line drawing, if we permit pipe-disk intersections.

show abstract

“…Finally, C is c-connected if G(ν) is connected, for each ν ∈ T [9,10]. Two important algorithms to draw clustered graphs using rectangular regions are described in [1,5].…”

Section: Background and Related Workmentioning

confidence: 99%

“…However, if the size of the squares is too small the edges incident with a high-degree node may appear too close to one another which we avoid by keeping a large angular resolution. Tree-like confluent graphs [15] and delta-confluent graphs [7] can also be drawn with angular resolution ≥ π/2, but they are limited to chordal bipartite graphs and distance hereditary graphs respectively, while our drawings can represent every confluent graph 1 . The remainder of the paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Confluent Drawing Algorithms Using Rectangular Dualization

Quercini

Ancona

2011

Graph Drawing

View full text Add to dashboard Cite

The need of effective drawings for non-planar dense graphs is motivated by the wealth of applications in which they occur, including social network analysis, security visualization and web clustering engines, just to name a few. One common issue graph drawings are affected by is the visual clutter due to the high number of (possibly intersecting) edges to display. Confluent drawings address this problem by bundling groups of edges sharing the same path, resulting in a representation with less edges and no edge intersections. In this paper we describe how to create a confluent drawing of a graph from its rectangular dual and we show two important advantages of this approach.

show abstract

Straight-Line Rectangular Drawings of Clustered Graphs

Abstract: We show that every c-planar clustered graph has a straight-line c-planar drawing in which each cluster is represented by an axis-parallel rectangle, thus solving a problem posed by Eades, Feng, Lin, and Nagamochi (Algorithmica 44 (1): 2006).

Cited by 15 publications

References 17 publications

Strip Planarity Testing for Embedded Planar Graphs

Strip Planarity Testing for Embedded Planar Graphs

Drawing Clustered Graphs on Disk Arrangements

Confluent Drawing Algorithms Using Rectangular Dualization

Contact Info

Product

Resources

About