Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.30
URN: urn:nbn:de:0030-drops-104343
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10434/
Dumitrescu, Adrian
A Product Inequality for Extreme Distances
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Abstract
Let p_1,...,p_n be n distinct points in the plane, and assume that the minimum inter-point distance occurs s_{min} times, while the maximum inter-point distance occurs s_{max} times. It is shown that s_{min} s_{max} <= (9/8)n^2 + O(n); this settles a conjecture of Erdös and Pach (1990).
BibTeX - Entry
@InProceedings{dumitrescu:LIPIcs:2019:10434,
author = {Adrian Dumitrescu},
title = {{A Product Inequality for Extreme Distances}},
booktitle = {35th International Symposium on Computational Geometry (SoCG 2019)},
pages = {30:1--30:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-104-7},
ISSN = {1868-8969},
year = {2019},
volume = {129},
editor = {Gill Barequet and Yusu Wang},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10434},
URN = {urn:nbn:de:0030-drops-104343},
doi = {10.4230/LIPIcs.SoCG.2019.30},
annote = {Keywords: Extreme distances, repeated distances}
}
| Keywords: | Extreme distances, repeated distances | |
| Seminar: | 35th International Symposium on Computational Geometry (SoCG 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 11.06.2019 |
