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An SPQR-Tree Approach to Decide Special Cases of Simultaneous Embedding with Fixed Edges

  • J. Joseph Fowler
  • Carsten Gutwenger
  • Michael Jünger
  • Petra Mutzel
  • Michael Schulz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)

Abstract

We present a linear-time algorithm for solving the simultaneous embedding problem with fixed edges (SEFE) for a planar graph and a pseudoforest (a graph with at most one cycle) by reducing it to the following embedding problem: Given a planar graph G, a cycle C of G, and a partitioning of the remaining vertices of G, does there exist a planar embedding in which the induced subgraph on each vertex partite of G ∖ C is contained entirely inside or outside C? For the latter problem, we present an algorithm that is based on SPQR-trees and has linear running time. We also show how we can employ SPQR-trees to decide SEFE for two planar graphs where one graph has at most two cycles and the intersection is a pseudoforest in linear time. These results give rise to our hope that our SPQR-tree approach might eventually lead to a polynomial-time algorithm for deciding the general SEFE problem for two planar graphs.

Keywords

Planar Graph Decision Algorithm Cyclic Order Expansion Graph Auxiliary Graph 
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 2009

Authors and Affiliations

  • J. Joseph Fowler
    • 1
  • Carsten Gutwenger
    • 2
  • Michael Jünger
    • 3
  • Petra Mutzel
    • 2
  • Michael Schulz
    • 3
  1. 1.Department of Computer ScienceUniversity of ArizonaUSA
  2. 2.Department of Computer ScienceTechnische Universität DortmundGermany
  3. 3.Department of Computer ScienceUniversity of CologneGermany

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