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A linear time algorithm to recognize clustered planar graphs and its parallelization

  • Elias Dahlhaus
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1380)

Abstract

We develop a linear time algorithm for the following problem: Given a graph G and a hierarchical clustering of the vertices such that all clusters induce connected subgraphs, determine whether G may be embedded into the plane such that no cluster has a hole.

This is an improvement to the O(n 2)-algorithm of Q.W. Feng et al. [6] and the algorithm of Lengauer [12] that operates in linear time on a replacement system. The size of the input of Lengauer's algorithm is not necessarily linear with respect to the number of vertices.

Keywords

Planar Graph Maximum Weight Dual Graph Connected Subgraph Linear Time Algorithm 
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 1998

Authors and Affiliations

  • Elias Dahlhaus
    • 1
    • 2
  1. 1.Department of Mathematics and Department of Computer ScienceUniversity of CologneGermany
  2. 2.Dept. of Computer ScienceUniversity of BonnGermany

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