DROPS

Document

DOI: 10.4230/LIPIcs.SoCG.2016.46

A Lower Bound on Opaque Sets

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

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

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.

Cite as

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)

Copy BibTex To Clipboard

@InProceedings{kawamura_et_al:LIPIcs.SoCG.2016.46,
  author =	{Kawamura, Akitoshi and Moriyama, Sonoko and Otachi, Yota and Pach, J\'{a}nos},
  title =	{{A Lower Bound on Opaque Sets}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{46:1--46:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.46},
  URN =		{urn:nbn:de:0030-drops-59386},
  doi =		{10.4230/LIPIcs.SoCG.2016.46},
  annote =	{Keywords: barriers; Cauchy-Crofton formula; lower bound; opaque sets}
}

Search Results

Documents authored by Moriyama, Sonoko

A Lower Bound on Opaque Sets

Abstract

Cite as

Thanks for your feedback!

Could not send message