Discrete & Computational Geometry

, Volume 7, Issue 4, pp 381–401 | Cite as

Area requirement and symmetry display of planar upward drawings

  • Giuseppe Di Battista
  • Roberto Tamassia
  • Ioannis G. Tollis


In this paper we investigate the problem of constructing planar straight-line drawings of acyclic digraphs such that all the edges flow in the same direction, e.g., from bottom to top. Our contribution is twofold. First we show the existence of a family of planar acyclic digraphs that require exponential area for any such drawing. Second, motivated by the preceding lower bound, we relax the straight-line constraint and allow bends along the edges. We present a linear-time algorithm that produces drawings of planarst-graphs with a small number of bends, asymptotically optimal area, and such that symmetries and isomorphisms of the digraph are displayed. If the digraph has no transitive edges, then the drawing obtained has no bends. Also, a variation of the algorithm produces drawings with exact minimum area.


Planar Graph Outgoing Edge Incoming Edge Isomorphic Subgraph Outerplanar Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Giuseppe Di Battista
    • 1
  • Roberto Tamassia
    • 2
  • Ioannis G. Tollis
    • 3
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”113 RomaItaly
  2. 2.Department of Computer ScienceBrown UniversityProvidenceUSA
  3. 3.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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