Lower bounds for weak epsilon-nets and stair-convexity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A00206593" target="_blank" >RIV/00216208:11320/09:00206593 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Lower bounds for weak epsilon-nets and stair-convexity
Original language description
We derive the first ever superlinear lower bounds for weak epsilon-nets (for fixed dimension $d$). We do this by showing that, if S is a finite grid of points in the plane that is suitably ``stretched' in the y-direction, then every weak 1/r-net for S must have size at least const.r log r. Our construction readily generalizes to arbitrary dimension: A suitably-stretched grid in R^d yields the lower bound const.r log^(d-1) r.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
PROCEEDINGS OF THE TWENTY-FIFTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SCG'09)
ISBN
978-1-60558-501-7
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
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Publisher name
ACM Press
Place of publication
New York
Event location
New York
Event date
Jan 1, 2009
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000267982900001