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Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

National ICT Australia Australia
Algorithmica (Impact Factor: 0.57). 12/2005; 44(1):1-32. DOI: 10.1007/s00453-004-1144-8
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ABSTRACT Hierarchical graphs and clustered graphs are useful non-classical 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 planar straight-line representation has not been solved completely.
In this paper we answer the question: does every planar hierarchical graph admit a planar straight-line
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
straight-line drawing with clusters drawn as convex polygons? We
provide a method for such drawings based on our algorithm for
hierarchical graphs.

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    • "We present an algorithm to construct a convex drawing of clustered planar graphs. Note that this extends the previous known results on straight-line drawings of connected clustered planar graphs [7]. This paper is organized as follows: Section 2 reviews basic terminology. "
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    ABSTRACT: Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI de- sign, CASE tools, software visualisation and visualisation of social networks and bi- ological networks. Straight-line drawing algorithms for hierarchical graphs and clus- tered graphs have been presented in (P. Eades, Q. Feng, X. Lin and H. Nagamochi, Straight-line drawing algorithms for hierarchical graphs and clustered graphs, Algo- rithmica, 44, pp. 1-32, 2006). A straight-line drawing is called a convex drawing if every facial cycle is drawn as a convex polygon. In this paper, it is proved that every internally triconnected hierarchical plane graph with the outer facial cycle drawn as a convex polygon admits a convex drawing. We present an algorithm which constructs such a drawing. We then extend our results to convex representations of clustered planar graphs. It is proved that every internally triconnected clustered plane graph with completely connected clustering structure admits a convex drawing. We present an algorithm to construct a convex drawing of clustered planar graphs.
    Journal of Discrete Algorithms 09/2010; 8(3):282-295. DOI:10.1016/j.jda.2009.05.003
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    • "In general, the visual representation is completely unaware of the way G C has been produced: this is a simpler setting than the one of e.g. [5] [11] in which the proposed algorithms aim at representing a socalled clustered graph. In this latter context, the ultimate goal is to visualize the complete original graph in a way that respects the (hierarchical) clustering structure. "
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