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Planarity Testing and Optimal Edge Insertion with Embedding Constraints

  • Carsten Gutwenger
  • Karsten Klein
  • Petra Mutzel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)

Abstract

Many practical applications demand additional restrictions on an admissible planar embedding. In particular, constraints on the permitted (clockwise) order of the edges around a vertex, like so-called side constraints, abound. In this paper, we introduce a set of hierarchical embedding constraints that also comprises side constraints. We present linear time algorithms for testing if a graph is ec-planar, i.e., admits a planar embedding satisfying the given embedding constraints, as well as for computing such an embedding. Moreover, we characterize the set of all possible ec-planar embeddings and consider the problem of finding a planar combinatorial embedding of a planar graph such that an additional edge can be inserted with the minimum number of crossings; we show that this problem can still be solved in linear time under the additional restrictions of embedding constraints.

Keywords

Planar Graph Linear Time Algorithm Expansion Graph Clockwise Order Planar Embedding 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Carsten Gutwenger
    • 1
  • Karsten Klein
    • 1
  • Petra Mutzel
    • 1
  1. 1.University of DortmundGermany

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