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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 ..."
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Cited by 71 (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.
Visualisations of Large ObjectOriented Systems
 In Software Visualization. WorldScientific
, 1995
"... The use of ternary diagrams to represent normalised call graph directions permit the succinct visualisations of objectoriented (OO) systems. Important features of such diagrams include (i) the ability to compare different objectoriented applications; and (ii) the potential ability to make value ju ..."
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Cited by 7 (2 self)
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The use of ternary diagrams to represent normalised call graph directions permit the succinct visualisations of objectoriented (OO) systems. Important features of such diagrams include (i) the ability to compare different objectoriented applications; and (ii) the potential ability to make value judgments about partially completed systems. Ternary diagrams also permit an overview of very large graphs. For example, we present here a visualisation of five OO applications comprising 1,643 vertices and 194,451 edges. 1 Introduction A call graph is a directed graph whose vertices represent basic data values and whose edges represent how those basic data values are passed to subroutines. An anonymous call graph is a call graph where all the vertices have been changed to anonymous variables (e.g. class0023) and the source of the call graph is not recorded with the graph. Call graphs offer a uniform view for a variety of programming systems. For example, the dependency network within a prop...
Clustered Graphs and Cplanarity
 In 3rd Annual European Symposium on Algorithms (ESA’95), LNCS 979
, 1995
"... In this paper, we introduce a new graph model known as clustered graphs, i.e. graphs with recursive clustering structures. This graph model has many applications in informational and mathematical sciences. In particular, we study Cplanarity of clustered graphs. Given a clustered graph, the Cplanar ..."
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Cited by 5 (2 self)
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In this paper, we introduce a new graph model known as clustered graphs, i.e. graphs with recursive clustering structures. This graph model has many applications in informational and mathematical sciences. In particular, we study Cplanarity of clustered graphs. Given a clustered graph, the Cplanarity testing problem is to determine whether the clustered graph can be drawn without edge crossings, or edgeregion crossings. In this paper, we present efficient algorithms for testing Cplanarity and finding Cplanar embeddings of clustered graphs. 1 Introduction Representing information visually, or by drawing graphs can greatly improve the effectiveness of user interfaces in many relational information systems [12, 17, 18, 5]. Developing algorithms for drawing graphs automatically and efficiently has become the interest of research for many computer scientists. Research in this area has been very active for the last decade. A recent survey citelabel13new of literature in this area inclu...
Drawing Clustered Graphs on . . .
 J. GRAPH ALGORITHMS APPL
, 1999
"... Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which pro ..."
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Cited by 3 (0 self)
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Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produces planar drawings of clustered graphs in a convention known as orthogonal grid rectangular cluster drawings. If the input graph has n vertices, then the algorithm produces in O(n) time a drawing with O(n²) area and at most 3 bends in each edge. This result is as good as existing results for classical planar graphs. Further, we show that our algorithm is optimal in terms of the number of bends per edge.
Recognizing Compound Planarity of Graphs
"... this paper, we introduce a practical and simple graph model called clustered graphs. We study, in particular, the planarity problem associated with this graph model. A clustered graph consists of a graph G and a recursive partitioning of the vertices of G. Each partition is known as a cluster of a ..."
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this paper, we introduce a practical and simple graph model called clustered graphs. We study, in particular, the planarity problem associated with this graph model. A clustered graph consists of a graph G and a recursive partitioning of the vertices of G. Each partition is known as a cluster of a subset of the vertices of G. Clustering appears in the diagrams produced in a wide number of applications areas, such as software engineering [22], knowledge representation [14], software visualization [21], idea organization [15], VLSI design [10], and general divide and conquer problem solving methodologies. Planarity is a much studied area for classical graphs. For example, the problem of minimizing edge crossings is proved to be NPhard [8]. However, efficient algorithms for testing whether a graph is planar (i.e. can be drawn without edge crossings) exist [12, 17, 5, 6]. In this paper, we introduce compound planarity (cplanarity), the planarity of clustered graphs. In a drawing of a clustered graph, vertices and edges are drawn as points and curves as usual. Clusters are drawn as simple closed curves that define closed regions of the plane. The region for each cluster contains the drawing of the subgraph induced by its vertices and no other vertices. A region for a cluster contains the regions for all its subclusters and does not intersect the region for any other cluster. A clustered graph is compoundplanar (cplanar) if it has a drawing with no crossings between distinct edges, or crossings between an edge and a region. Note that the planarity of the underlying graph does not