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Testing Simultaneous Planarity When the Common Graph Is 2-Connected

  • Bernhard Haeupler
  • Krishnam Raju Jampani
  • Anna Lubiw
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6507)

Abstract

Two planar graphs G 1 and G 2 sharing some vertices and edges are simultaneously planar if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether simultaneous planarity can be tested efficiently. We give a linear-time algorithm to test simultaneous planarity when the two graphs share a 2-connected subgraph. Our algorithm extends to the case of k planar graphs where each vertex [edge] is either common to all graphs or belongs to exactly one of them.

Keywords

Simultaneous Embedding Planar Graph PQ Tree Graph Drawing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bernhard Haeupler
    • 1
  • Krishnam Raju Jampani
    • 2
  • Anna Lubiw
    • 2
  1. 1.CSAIL, Dept. of Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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