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.
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© 1998 Springer-Verlag Berlin Heidelberg
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Dahlhaus, E. (1998). A linear time algorithm to recognize clustered planar graphs and its parallelization. In: Lucchesi, C.L., Moura, A.V. (eds) LATIN'98: Theoretical Informatics. LATIN 1998. Lecture Notes in Computer Science, vol 1380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054325
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DOI: https://doi.org/10.1007/BFb0054325
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