Approximate inclusion-exclusion
Nathan Linial, Noam Nisan · 1990
The Inclusion-Exclusion formula expresses the size of a union of a family of sets in terms of the sizes of intersections of all subfamilies.This paper considers approximating the size of the union when intersection sizes are known for only some of the subfamilies, or when these quantities are given to within some error, or both.In particular, we consider the case when all k-wise intersections axe given for every k ft(v/'ff ) it is shown how to approximate the size of the union_to within a multiplicative factor of 1 :t: e -a(g/'/'a).When the sizes of all intersections are only given approximately, good bounds are derived on how well the size of the union may be approximated.Several applications for boolean function are mentioned in conclusion.