Uniform decompositions of polytopes

• Autorzy: Daniel Berend , Luba Bromberg
• Języki publikacji: EN

Abstrakty

EN

We design a method of decomposing convex polytopes into simpler polytopes. This decomposition yields a way of calculating exactly the volume of the polytope, or, more generally, multiple integrals over the polytope, which is equivalent to the way suggested in Schechter, based on Fourier-Motzkin elimination (Schrijver). Our method is applicable for finding uniform decompositions of certain natural families of polytopes. Moreover, this allows us to find algorithmically an analytic expression for the distribution function of a random variable of the form $∑_{i=1}^{d}c_{i}X_{i}$, where $(X₁,..., X_{d})$ is a random vector, uniformly distributed in a polytope.

Kategorie tematyczne

• 65D18: Computer graphics, image analysis, and computational geometry
• 60-08: Computational methods (not classified at a more specific level)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2006
• Tom: 33
• Numer: 2
• Strony: 243-252

Daty

wydano

2006

Twórcy

autor

Daniel Berend

• Departments of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

autor

Luba Bromberg

• Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

Identyfikatory

DOI

10.4064/am33-2-7