Complexity Results for Three-Dimensional Orthogonal Graph Drawing

(Extended Abstract)
  • Maurizio Patrignani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)


We introduce the 3SAT reduction framework which can be used to prove the NP-hardness of finding three-dimensional orthogonal drawings with specific constraints. We use it to show that finding a drawing of a graph whose edges have a fixed shape is NP-hard. Also, it is NP-hard finding a drawing of a graph with nodes at prescribed positions when a maximum of two bends per edge is allowed. We comment on the impact of these results on the two open problems of determining whether a graph always admits a 3D orthogonal drawing with at most two bends per edge and of characterizing orthogonal shapes admitting a drawing without intersections.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Maurizio Patrignani
    • 1
  1. 1.Università di Roma TreItaly

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