reference biblio

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Remy Thomasse 2014-06-26 10:43:21 +02:00
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@ -151908,3 +151908,13 @@ pages = {179--189}
year={2010}
}
@TechReport{Devillers2014Generator
, author = "Olivier Devillers and Philippe Duchon and R{\'e}my Thomasse"
, title = "A generator of random convex polygon in a disc"
, institution = "INRIA"
, type = "Research Report"
, number = "RR-8467"
, month = "Feb"
, year = "2014"
, url = "http://hal.inria.fr/hal-00943409"
}

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@ -27,7 +27,7 @@ The generated polygon will have an average number of vertices \f$ n^\frac{1}{3}(
\cgalHeading{Implementation}
The implementation is based on an incremental construction of a convex hull. At each step, we choose a number of points to pick uniformly at random in the disc. Then, a subset of these points, that won't change the convex hull, is evaluated using a Binomial law.
As these points won't be generated, the time and size complexities are reduced.
As these points won't be generated, the time and size complexities are reduced \cgalCite{Devillers2014Generator}.
A tradeoff between time and memory is provided with the option `fast`, true by default. Using the `fast` option, both time and size expected complexities are \f$O\left(n^\frac{1}{3}\log^\frac{2}{3}n \right)\f$.
If this option is disabled, the expected size complexity becomes \f$O\left(n^\frac{1}{3}\right)\f$ but the expected time complexity becomes \f$O\left(n^\frac{1}{3}\log^2 n \right)\f$.