A note on approximate inclusion-exclusion

Avraham A. Melkman; Solomon E. Shimony

doi:10.1016/S0166-218X(96)00048-0

A note on approximate inclusion-exclusion

Avraham A. Melkman, Solomon E. Shimony

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let A_i, i = l, . . . , n, be a sequence of sets, and for S ⊆[n] set as := | ∩_i∈s A_i |. Kahn, Linial and Samorodnitsky have recently shown that if it is known that u := | ∪_i=l ⁿ, A_i | < 2^n-l then u can be determined uniquely from a knowledge of the values of a_s for all S ≠ [n]. Since their proof was existential they posed the question of finding an adaptive procedure for determining u. Here we present such an algorithm.

Original language	English
Pages (from-to)	23-26
Number of pages	4
Journal	Discrete Applied Mathematics
Volume	73
Issue number	1
DOIs	https://doi.org/10.1016/S0166-218X(96)00048-0
State	Published - 21 Feb 1997

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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abstract = "Let Ai, i = l, . . . , n, be a sequence of sets, and for S ⊆[n] set as := | ∩i∈s Ai |. Kahn, Linial and Samorodnitsky have recently shown that if it is known that u := | ∪i=l n, Ai | < 2n-l then u can be determined uniquely from a knowledge of the values of as for all S ≠ [n]. Since their proof was existential they posed the question of finding an adaptive procedure for determining u. Here we present such an algorithm.",

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AB - Let Ai, i = l, . . . , n, be a sequence of sets, and for S ⊆[n] set as := | ∩i∈s Ai |. Kahn, Linial and Samorodnitsky have recently shown that if it is known that u := | ∪i=l n, Ai | < 2n-l then u can be determined uniquely from a knowledge of the values of as for all S ≠ [n]. Since their proof was existential they posed the question of finding an adaptive procedure for determining u. Here we present such an algorithm.

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A note on approximate inclusion-exclusion

Abstract

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