On the computational complexity of upward and rectilinear planarity testing

  • Ashim Garg
  • Roberto Tamassia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)


A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical segment, and no two edges cross. Testing upward planarity and rectilinear planarity are fundamental problems in the effective visualization of various graph and network structures. In this paper we show that upward planarity testing and rectilinear planarity testing are NP-complete problems. We also show that it is NP-hard to approximate the minimum number of bends in a planar orthogonal drawing of an n-vertex graph with an O(n1−∈) error, for any ∈>0.


Planar Graph Planarity Testing Planar Drawing Acyclic Digraph Capacity Range 
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 Berlin Heidelberg 1995

Authors and Affiliations

  • Ashim Garg
    • 1
  • Roberto Tamassia
    • 1
  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA

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