LIPIcs.SoCG.2023.62.pdf
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Godzilla Onions: A Skit and Applet to Explain Euclidean Half-Plane Fractional Cascading (Media Exposition)
Authors
Christopher J. Tralie 
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Volume:
39th International Symposium on Computational Geometry (SoCG 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-06-09
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Cite As Get BibTex
Richard Berger, Vincent Ha, David Kratz, Michael Lin, Jeremy Moyer, and Christopher J. Tralie. Godzilla Onions: A Skit and Applet to Explain Euclidean Half-Plane Fractional Cascading (Media Exposition). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 62:1-62:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.SoCG.2023.62
Abstract
We provide a skit and an applet to illustrate fractional cascading in the context of half-plane range search for points in the Euclidean plane, which takes O(log N + h) output-sensitive time. In the video, a group of news anchors struggles to find the correct data structure to efficiently send out an early warning to the residents of Philadelphia who will be overtaken by a marching line of Godzillas. After exploring several options, the group eventually settles on onions and fractional cascading, only to discover that they themselves are in the line of fire! In the applet, we show step by step details of preprocessing to build the onions with fractional cascading and the subsequent query of the "Godzilla line" against the onion layers. Our video skit and applet can be found at https://ctralie.github.io/GodzillaOnions/
Subject Classification
ACM Subject Classification
- Human-centered computing → Visualization toolkits
- Theory of computation → Randomness, geometry and discrete structures
Keywords
- convex hulls
- onions
- fractional cascading
- visualization
- d3
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References
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Michael Bostock, Vadim Ogievetsky, and Jeffrey Heer. D³ data-driven documents. IEEE Transactions on Visualization and Computer Graphics, 17(12):2301-2309, 2011.
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Bernard Chazelle. On the convex layers of a planar set. IEEE Transactions on Information Theory, 31(4):509-517, 1985.
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Ketan Dalal. Counting the onion. Random Structures & Algorithms, 24(2):155-165, 2004.
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Leonidas Guibas and Bernard Chazelle. Fractional cascading: I. a data structuring technique. Algorithmica, 1:133-162, 1986.
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