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Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

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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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Authors and Affiliations

  1. School of Information Technologies, University of Sydney, NSW 2006, Australia

    Peter Eades & Qingwen Feng

  2. National ICT, Australia

    Peter Eades & Xuemin Lin

  3. School of Computer Science and Engineering, University of New SouthWales, Sydney,NSW2052, Australia

    Xuemin Lin

  4. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University Yoshida Honmachi, Sakyo, Kyoto 606-8501,, Japan

    Hiroshi Nagamochi

Authors
  1. Peter Eades
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  2. Qingwen Feng
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  3. Xuemin Lin
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  4. Hiroshi Nagamochi
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Corresponding authors

Correspondence to Peter Eades, Qingwen Feng, Xuemin Lin or Hiroshi Nagamochi.

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Eades, P., Feng, Q., Lin, X. et al. Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs. Algorithmica 44, 1–32 (2006). https://doi.org/10.1007/s00453-004-1144-8

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  • DOI: https://doi.org/10.1007/s00453-004-1144-8

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