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Empty non-convex and convex four-gons in random point sets

Autor
Fabila, R.; Huemer, C.; Mitsche, D.
Tipus d'activitat
Article en revista
Revista
Studia scientiarum mathematicarum hungarica
Data de publicació
2015-03-01
Volum
52
Número
1
Pàgina inicial
52
Pàgina final
64
DOI
https://doi.org/10.1556/SScMath.52.2015.1.1301 Obrir en finestra nova
Projecte finançador
Morfología geométrica computacional.
Repositori
http://hdl.handle.net/2117/27964 Obrir en finestra nova
Resum
Let S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon is called empty if it contains no points of S in its interior. We show that the expected number of empty non-convex four-gons with vertices from S is 12 n(2) log n + o(n(2) log n) and the expected number of empty convex four-gons with vertices from S is Theta(n(2)).
Citació
Fabila, R.; Huemer, C.; Mitsche, D. Empty non-convex and convex four-gons in random point sets. "Studia scientiarum mathematicarum hungarica", 01 Març 2015, vol. 52, núm. 1, p. 52-64.
Paraules clau
Random Point Set, Empty Four-gon, Polygon, Geometric Probability, N-random Points, Probability, Triangles, Position, Polygons, Number, Holes
Grup de recerca
DCCG - Grup de recerca en geometria computacional, combinatoria i discreta

Participants

  • Fabila Monroy, Ruy  (autor)
  • Huemer, Clemens  (autor)
  • Mitsche, Dieter  (autor)

Arxius