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Grouping and Querying: A Paradigm to Get Output-Sensitive Algorithms

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Discrete and Computational Geometry (JCDCG 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1763))

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Abstract

In this paper, we review and analyze the complexity of a paradigm called grouping-and-querying which has been used in the past for computing convex hulls of points or objects on the plane, maximal and convex layer decompositions, lower envelopes of functions, etc. Then, we present new results concerning the computation of: (i) a transversal set for various families of geometric objects, (ii) a few (not necessarily connected) cells of a Voronoi diagram: Let \(\mathcal{S}\) be a set of n points of the Euclidean plane \(\mathbb{E}^2\), we give an O(n log h) time algorithm for computing the Voronoi cells of the sites \(\mathcal{S}'\subseteq\mathcal{S}\), where h is the output-size. We extend this approach to higher dimensions.

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Authors and Affiliations

  1. SONY Computer Science Laboratories Inc., Japan

    Frank Nielsen

Authors
  1. Frank Nielsen
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku Tokio, Japan

    Jin Akiyama

  2. Ibaraki University, Nakanarusawa, 316-8511, Hitachi Ibaraki, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido, Shimizu, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2000 Springer-Verlag Berlin Heidelberg

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Nielsen, F. (2000). Grouping and Querying: A Paradigm to Get Output-Sensitive Algorithms. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_21

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  • DOI: https://doi.org/10.1007/978-3-540-46515-7_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67181-7

  • Online ISBN: 978-3-540-46515-7

  • eBook Packages: Springer Book Archive

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