Inclusion-exclusion formulas from independent complexes

Authors:
Dominique Attali;Herbert Edelsbrunner
Affiliations:
Domaine Universitaire, BP;Duke University, Durham, NC
Venue:
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Year:
2005

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Abstract

Using inclusion-exclusion, we can write the indicator function of a union of finitely many balls as an alternating sum of indicator functions of common intersections of balls. We exhibit abstract simplicial complexes that correspond to minimal inclusion-exclusion formulas. They include the dual complex, as defined in [2], and are characterized by the independence of their simplices and by geometric realizations with the same underlying space as the dual complex.