A lower bound on opaque sets

Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi, János Pach

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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.

Original languageEnglish
Title of host publication32nd International Symposium on Computational Geometry, SoCG 2016
EditorsSandor Fekete, Anna Lubiw
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages46.1-46.10
ISBN (Electronic)9783959770095
DOIs
Publication statusPublished - Jun 1 2016
Event32nd International Symposium on Computational Geometry, SoCG 2016 - Boston, United States
Duration: Jun 14 2016Jun 17 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume51
ISSN (Print)1868-8969

Other

Other32nd International Symposium on Computational Geometry, SoCG 2016
CountryUnited States
CityBoston
Period6/14/166/17/16

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Kawamura, A., Moriyama, S., Otachi, Y., & Pach, J. (2016). A lower bound on opaque sets. In S. Fekete, & A. Lubiw (Eds.), 32nd International Symposium on Computational Geometry, SoCG 2016 (pp. 46.1-46.10). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 51). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SoCG.2016.46

A lower bound on opaque sets. / Kawamura, Akitoshi; Moriyama, Sonoko; Otachi, Yota; Pach, János.

32nd International Symposium on Computational Geometry, SoCG 2016. ed. / Sandor Fekete; Anna Lubiw. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2016. p. 46.1-46.10 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 51).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kawamura, A, Moriyama, S, Otachi, Y & Pach, J 2016, A lower bound on opaque sets. in S Fekete & A Lubiw (eds), 32nd International Symposium on Computational Geometry, SoCG 2016. Leibniz International Proceedings in Informatics, LIPIcs, vol. 51, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 46.1-46.10, 32nd International Symposium on Computational Geometry, SoCG 2016, Boston, United States, 6/14/16. https://doi.org/10.4230/LIPIcs.SoCG.2016.46
Kawamura A, Moriyama S, Otachi Y, Pach J. A lower bound on opaque sets. In Fekete S, Lubiw A, editors, 32nd International Symposium on Computational Geometry, SoCG 2016. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2016. p. 46.1-46.10. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.SoCG.2016.46
Kawamura, Akitoshi ; Moriyama, Sonoko ; Otachi, Yota ; Pach, János. / A lower bound on opaque sets. 32nd International Symposium on Computational Geometry, SoCG 2016. editor / Sandor Fekete ; Anna Lubiw. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2016. pp. 46.1-46.10 (Leibniz International Proceedings in Informatics, LIPIcs).
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