TY - GEN

T1 - Approximate Inclusion-Exclusion

AU - Linial, Nathan

AU - Nisan, Noam

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025106674&partnerID=8YFLogxK

U2 - 10.1145/100216.100250

DO - 10.1145/100216.100250

M3 - Conference contribution

AN - SCOPUS:0025106674

SN - 0897913612

SN - 9780897913614

T3 - Proc 22nd Annu ACM Symp Theory Comput

SP - 260

EP - 270

BT - Proc 22nd Annu ACM Symp Theory Comput

PB - Publ by ACM

T2 - Proceedings of the 22nd Annual ACM Symposium on Theory of Computing

Y2 - 14 May 1990 through 16 May 1990

ER -