Fast parallel algorithms for the subgraph homeomorphism and the subgraph isomorphism problem for classes of planar graphs

  • Andrzej Lingas
  • Andrzej Proskurowski
Session 2 Graph Algorithms & Geometric Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 287)


We consider the problems of subgraph homeomorphism with fixed pattern graph, recognition, and subgraph isomorphism for some classes of planar graphs. Following the results of Robertson and Seymour on forbidden minor characterization, we show that the problems of fixed subgraph homeomorphism and recognition for any family of planar graphs closed under minor taking are in NC (i.e., they can be solved by an algorithm running in poly-log time using polynomial number of processors). We also show that the related subgraph isomorphism problem for biconnected outerplanar graphs is in NC. This is the first example of a restriction of subgraph isomorphism to a non-trivial graph family admitting an NC algorithm.


Planar Graph Input Graph Recursive Call Simple Polygon Subgraph Isomorphism 
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 1987

Authors and Affiliations

  • Andrzej Lingas
    • 1
  • Andrzej Proskurowski
    • 2
  1. 1.Department of Computer and Information ScienceLinköping UniversityLinköpingSweden
  2. 2.Department of Computer and Information ScienceUniversity of OregonEugeneUSA

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