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

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


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.


Convex Hull High Dimension Problem Complexity Computer Graphic 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 2000

Authors and Affiliations

  • Frank Nielsen
    • 1
  1. 1.SONY Computer Science Laboratories Inc.Japan

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