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StraightLine Drawing Algorithms for Hierarchical Graphs and Clustered Graphs
 Algorithmica
, 1999
"... Hierarchical graphs and clustered graphs are useful nonclassical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualizatio ..."
Abstract

Cited by 59 (12 self)
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Hierarchical graphs and clustered graphs are useful nonclassical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualization, and VLSI design. Drawing algorithms for hierarchical graphs have been well investigated. However, the problem of straightline representation has not been solved completely. In this paper, we answer the question: does every planar hierarchical graph admit a planar straightline hierarchical drawing? We present an algorithm that constructs such drawings in linear time. Also, we answer a basic question for clustered graphs, that is, does every planar clustered graph admit a planar straightline drawing with clusters drawn as convex polygons? We provide a method for such drawings based on our algorithm for hierarchical graphs.
Completely connected clustered graphs
 IN PROC. 29TH INTL. WORKSHOP ON GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE (WG 2003), VOLUME 2880 OF LNCS
, 2003
"... Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove ..."
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Cited by 14 (1 self)
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Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove that a completely connected clustered graph is cplanar if and only if the underlying graph is planar. Further, we investigate the influence of the root of the inclusion tree to the choice of the outer face of the underlying graph and vice versa.
Clustering Cycles into Cycles of Clusters
, 2005
"... In this paper we study simple families of clustered graphs that are highly non connected. We start by studying 3cluster cycles, that are clustered graphs such that the underlying graph is a simple cycle and there are three clusters all at the same level. We show that in this case testing the cplan ..."
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Cited by 10 (5 self)
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In this paper we study simple families of clustered graphs that are highly non connected. We start by studying 3cluster cycles, that are clustered graphs such that the underlying graph is a simple cycle and there are three clusters all at the same level. We show that in this case testing the cplanarity can be done efficiently and give an efficient drawing algorithm. Also, we characterize 3cluster cycles in terms of formal grammars. Finally, we generalize the results on 3cluster cycles considering clustered graphs that have a cycle structure at each level of the inclusion tree. Even in this case we show efficient cplanarity testing and drawing algorithms.
Cplanarity of extrovert clustered graphs
 In Graph Drawing
, 2005
"... Abstract. A clustered graph has its vertices grouped into clusters in a hierarchical way via subset inclusion, thereby imposing a tree structure on the clustering relationship. The cplanarity problem is to determine if such a graph can be drawn in a planar way, with clusters drawn as nested regions ..."
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Cited by 6 (1 self)
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Abstract. A clustered graph has its vertices grouped into clusters in a hierarchical way via subset inclusion, thereby imposing a tree structure on the clustering relationship. The cplanarity problem is to determine if such a graph can be drawn in a planar way, with clusters drawn as nested regions and with each edge (drawn as a curve between vertex points) crossing the boundary of each region at most once. Unfortunately, as with the graph isomorphism problem, it is open as to whether the cplanarity problem is NPcomplete or in P. In this paper, we show how to solve the cplanarity problem in polynomial time for a new class of clustered graphs, which we call extrovert clustered graphs. This class is quite natural (we argue that it captures many clustering relationships that are likely to arise in practice) and includes the clustered graphs tested in previous work by Dahlhaus, as well as Feng, Eades, and Cohen. Interestingly, this class of graphs does not include, nor is it included by, a class studied recently by Gutwenger et al.; therefore, this paper offers an alternative advancement in our understanding of the efficient drawability of clustered graphs in a planar way. Our testing algorithm runs in O(n 3) time and implies an embedding algorithm with the same time complexity. 1
On embedding a cycle in a plane graph
 PROC. 13TH INT. SYMP. GRAPH DRAWING (GD’05), VOLUME 3843 OF LNCS
, 2006
"... ..."
Overlapping Cluster Planarity
, 2008
"... This paper investigates a new direction in the area of cluster planarity by addressing the following question: Let G be a graph along with a hierarchy of vertex clusters, where clusters can partially intersect. Does G admit a drawing where each cluster is inside a simple closed region, no two edges ..."
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Cited by 4 (0 self)
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This paper investigates a new direction in the area of cluster planarity by addressing the following question: Let G be a graph along with a hierarchy of vertex clusters, where clusters can partially intersect. Does G admit a drawing where each cluster is inside a simple closed region, no two edges intersect, and no edge intersects a region twice? We investigate the interplay between this problem and the classical cluster planarity testing problem where clusters are not allowed to partially intersect. Characterizations, models, and algorithms are discussed.
Characterizing Families of Cuts That Can Be Represented by AxisParallel Rectangles
"... A drawing of a family of cuts of a graph is an augmented drawing of the graph such that every cut is represented by a simple closed curve and vice versa. ..."
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Cited by 1 (1 self)
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A drawing of a family of cuts of a graph is an augmented drawing of the graph such that every cut is represented by a simple closed curve and vice versa.
CPlanarity of cconnected clustered graphs
, 2008
"... We present the first characterization of cplanarity for cconnected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchies of the triconnected and biconnected components of the underlying graph. Based on such a characterization, we ..."
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Cited by 1 (1 self)
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We present the first characterization of cplanarity for cconnected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchies of the triconnected and biconnected components of the underlying graph. Based on such a characterization, we provide a lineartime cplanarity testing and embedding algorithm for cconnected clustered graphs. The algorithm is reasonably easy to implement, since it exploits as building blocks simple algorithmic tools like the computation of lowest common ancestors, minimum and maximum spanning trees, and counting sorts. It also makes use of wellknown data structures as SPQRtrees and BCtrees. If the test fails, the algorithm identifies a structural element responsible for the noncplanarity of the input clustered graph.
Clustering Cycles into Cycles of Clusters (Extended Abstract – Long Regular Paper)
"... In this paper we study the clustered graphs whose underlying graph is a cycle. This is a simple family of clustered graphs that are “highly non connected”. We start by studying 3cluster cycles, that are clustered graphs such that the underlying graph is a simple cycle and there are three clusters a ..."
Abstract
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In this paper we study the clustered graphs whose underlying graph is a cycle. This is a simple family of clustered graphs that are “highly non connected”. We start by studying 3cluster cycles, that are clustered graphs such that the underlying graph is a simple cycle and there are three clusters all at the same level. We show that in this case testing the cplanarity can be done efficiently and give an efficient drawing algorithm. Also, we characterize 3cluster cycles in terms of formal grammars. Finally, we generalize the results on 3cluster cycles considering clustered graphs that at each level of the inclusion tree have a cycle structure. Even in this case we show efficient cplanarity testing and drawing algorithms.