On the Beer Index of Convexity and Its Variants
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10313927" target="_blank" >RIV/00216208:11320/15:10313927 - isvavai.cz</a>
Result on the web
<a href="http://drops.dagstuhl.de/opus/volltexte/2015/5122/" target="_blank" >http://drops.dagstuhl.de/opus/volltexte/2015/5122/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.406" target="_blank" >10.4230/LIPIcs.SOCG.2015.406</a>
Alternative languages
Result language
angličtina
Original language name
On the Beer Index of Convexity and Its Variants
Original language description
Let S be a subset of R^d with finite positive Lebesgue measure. The Beer index of convexity b(S) of S is the probability that two points of S chosen uniformly independently at random see each other in S. The convexity ratio c(S) of S is the Lebesgue measure of the largest convex subset of S divided by the Lebesgue measure of S. We investigate a relationship between these two natural measures of convexity of S. We show that every subset S of the plane with simply connected components satisfies b(S) LESS-THAN OR EQUAL TO alpha c(S) for an absolute constant alpha, provided b(S) is defined. This implies an affirmative answer to the conjecture of Cabello et al. asserting that this estimate holds for simple polygons. We also consider higher-order generalizations of b(S). For 1 LESS-THAN OR EQUAL TO k LESS-THAN OR EQUAL TO d, the k-index of convexity b_k(S) of a subset S of R^d is the probability that the convex hull of a (k+1)-tuple of points chosen uniformly independently at random from S i
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/GA14-14179S" target="_blank" >GA14-14179S: Algorithmic, structural and complexity aspects of configurations in the plane</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
31st International Symposium on Computational Geometry
ISBN
978-3-939897-83-5
ISSN
1868-8969
e-ISSN
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Number of pages
15
Pages from-to
406-420
Publisher name
LIPICS
Place of publication
Dagstuhl
Event location
Eindhoven, The Netherlands
Event date
Jun 22, 2015
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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