On the computational complexity of upward and rectilinear planarity testing

  • Ashim Garg
  • Roberto Tamassia
Conference paper

DOI: 10.1007/3-540-58950-3_384

Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)
Cite this paper as:
Garg A., Tamassia R. (1995) On the computational complexity of upward and rectilinear planarity testing. In: Tamassia R., Tollis I.G. (eds) Graph Drawing. GD 1994. Lecture Notes in Computer Science, vol 894. Springer, Berlin, Heidelberg

Abstract

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.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

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

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