Weak Dominance Drawings for Directed Acyclic Graphs

  • Evgenios M. Kornaropoulos
  • Ioannis G. Tollis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)

Abstract

The dominance drawing method has many important aesthetic properties, including small number of bends, good vertex placement, and symmetry display [1]. Furthermore, it encapsulates the aspect of characterizing the transitive closure of the digraph by means of a geometric dominance relation among the vertices. A dominance drawing Γ of a planar st-graph G is a drawing, such that for any two vertices u and v there is a directed path from u to v in G if and only if X(u) ≤ X(v) and Y(u) ≤ Y(v) in Γ [1]. Here we study weak dominance drawings where for any two vertices u and v if there is a directed path from u to v in G then X(u) ≤ X(v) and Y(u) ≤ Y(v) in Γ.

References

  1. 1.
    Di Battista, G., Tamassia, R., Tollis, I.G.: Area Requirement and Symmetry Display of Planar Upward Drawings. Discrete and Comput. Geom. 7(4), 381–401 (1992)MathSciNetMATHCrossRefGoogle Scholar
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    Eades, P., ElGindy, H., Houle, M., Lenhart, B., Miller, M., Rappaport, D., Whitesides, S.: Dominance Drawings of Bipartite Graphs (1993) (manuscript)Google Scholar
  3. 3.
    Kornaropoulos, E.M., Tollis, I.G.: Weak Dominance Drawings and Linear Extension Diameter, arXiv:1108.1439 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Evgenios M. Kornaropoulos
    • 1
    • 2
  • Ioannis G. Tollis
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of CreteHeraklionGreece
  2. 2.Institute of Computer ScienceFoundation for Research and Technology-HellasGreece

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