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Algorithms for determining the geometrical congruity in two and three dimensions

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Algorithms and Computation (ISAAC 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 650))

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Abstract

This paper discusses the problem of determining the geometrical congruity. O(n log n) time algorithms for point sets in three dimensions and for graphs whose vertices are points in three dimensions are presented, respectively. They are based on Sugihara's algorithm for determining the congruity of polyhedra. Moreover, an O(log n) time O(n) processors parallel algorithm for graphs in two dimensions which works on a CRCW PRAM is presented. In this algorithm, the original problem is transformed into the string matching problem. All the algorithms are optimal and can be modified for computing the canonical forms.

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Authors and Affiliations

  1. Mechanical Engineering Laboratory, 1-2 Namiki, Tsukuba, 305, Ibaraki, Japan

    Tatsuya Akutsu

Authors
  1. Tatsuya Akutsu
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Editor information

Toshihide Ibaraki Yasuyoshi Inagaki Kazuo Iwama Takao Nishizeki Masafumi Yamashita

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© 1992 Springer-Verlag Berlin Heidelberg

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Akutsu, T. (1992). Algorithms for determining the geometrical congruity in two and three dimensions. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_81

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  • DOI: https://doi.org/10.1007/3-540-56279-6_81

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56279-5

  • Online ISBN: 978-3-540-47501-9

  • eBook Packages: Springer Book Archive

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