Approximate Inclusion-Exclusion

Nathan Linial*, Noam Nisan

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


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 are given for every k ≤ K. It turns out that the answer changes in a significant, way around K = √n: if K ≤ O(√n) then any approximation may err by a factor of Θ(n/K2), while if K ≥ Ω(√n) it is shown how to approximate the size of the union to within a multiplicative factor of 1 ± e-Ω(K/√n). 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.

Original languageAmerican English
Title of host publicationProc 22nd Annu ACM Symp Theory Comput
PublisherPubl by ACM
Number of pages11
ISBN (Print)0897913612, 9780897913614
StatePublished - 1990
Externally publishedYes
EventProceedings of the 22nd Annual ACM Symposium on Theory of Computing - Baltimore, MD, USA
Duration: 14 May 199016 May 1990

Publication series

NameProc 22nd Annu ACM Symp Theory Comput


ConferenceProceedings of the 22nd Annual ACM Symposium on Theory of Computing
CityBaltimore, MD, USA


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