A Lower Bound on Opaque Sets

Kawamura, Akitoshi; Moriyama, Sonoko; Otachi, Yota; Pach, János

doi:10.4230/LIPIcs.SoCG.2016.46

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A Lower Bound on Opaque Sets

Authors Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, János Pach

Part of: Volume: 32nd International Symposium on Computational Geometry (SoCG 2016)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Computational Geometry (SoCG)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2016-06-10

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Document Identifiers

DOI: 10.4230/LIPIcs.SoCG.2016.46
URN: urn:nbn:de:0030-drops-59386

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Keywords

barriers; Cauchy-Crofton formula; lower bound; opaque sets

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Abstract

It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This is the first improvement on the lower bound of 2 by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle.

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Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, and János Pach. A Lower Bound on Opaque Sets. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 46:1-46:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.SoCG.2016.46

Author Details

Akitoshi Kawamura

Sonoko Moriyama

Yota Otachi

János Pach

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