A Simple Linear-Time Algorithm for Computing the Centroid and Canonical Form of a Plane Graph and Its Applications

Authors Tatsuya Akutsu, Colin de la Higuera, Takeyuki Tamura

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Tatsuya Akutsu
  • Bioinformatics Center, Institute for Chemical Research, Kyoto University, Kyoto 611-0011, Japan
Colin de la Higuera
  • LINA, UMR CNRS 6241, Universitéde Nantes, 44322 Nantes Cedex 03, France
Takeyuki Tamura
  • Bioinformatics Center, Institute for Chemical Research, Kyoto University, Kyoto 611-0011, Japan

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Tatsuya Akutsu, Colin de la Higuera, and Takeyuki Tamura. A Simple Linear-Time Algorithm for Computing the Centroid and Canonical Form of a Plane Graph and Its Applications. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 10:1-10:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We present a simple linear-time algorithm for computing the topological centroid and the canonical form of a plane graph. Although the targets are restricted to plane graphs, it is much simpler than the linear-time algorithm by Hopcroft and Wong for determination of the canonical form and isomorphism of planar graphs. By utilizing a modified centroid for outerplanar graphs, we present a linear-time algorithm for a geometric version of the maximum common connected edge subgraph (MCCES) problem for the special case in which input geometric graphs have outerplanar structures, MCCES can be obtained by deleting at most a constant number of edges from each input graph, and both the maximum degree and the maximum face degree are bounded by constants.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Plane graph
  • Graph isomorphism
  • Maximum common subgraph


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