Inclusion-exclusion formulas from independent complexes
type: Item
instance of: scholarly article
title: Inclusion-exclusion formulas from independent complexes
zbMATH Open document ID: 1114.52017
author: D. Attali
author: Herbert Edelsbrunner
published in: Discrete \& Computational Geometry
publication date: 2007-02-14T00:00:00Z
review text: The volume of a union of spheres has many practical applications. Unfortunately, the general inclusion-exclusion principle becomes exponentially difficult to use as the number of spheres increases. This can be overcome if certain terms in the inclusion-exclusion principle are ignored. Methods of determining which terms to ignore, via Delauney triangulations and dual complexes have been derived in the past. This article generalises some such methods. The result is a method of deriving an abstract simplicial complex from a collection of spheres, and a way to use this complex to determine a formula for the volume of the union of this collection of spheres. Careful proofs are given of the validity of the methods, and some suggestions are given on how the results could be extended to unions of other collections of other shapes (ellipsoids, for example).
Mathematics Subject Classification ID: 52C45
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52B55
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 5126701
zbMATH Keywords: inclusion-exclusion
zbMATH Keywords: union of spheres
zbMATH Keywords: simplicial complex
zbMATH Keywords: Delauney triangulation
reviewed by: Michael I. Hartley
MaRDI profile type: Publication
full work available at URL: s00454-006-1274-7
OpenAlex ID: W1965201771
DOI: 10.1007/S00454-006-1274-7
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description: scientific article; zbMATH DE number 5126701