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Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

National ICT Australia Australia; School of Computer Science and Engineering, University of New SouthWales, Sydney,NSW2052 Australia Australia
Algorithmica (Impact Factor: 0.49). 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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