Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions

  title={Approximate Inclusion-Exclusion for Arbitrary Symmetric Functions},
  author={Alexander A. Sherstov},
  booktitle={Computational Complexity Conference},
Let A_1,..., A_n be events in a probability space. The approximate inclusion-exclusion problem, due to Linial and Nisan (1990), is to estimate Prob [A_1 OR ... OR A_n] given Prob [AND_{i in S} A_i] for |S|{0,1} is a given symmetric function. (In the Linial-Nisan problem, f=OR.). We solve this general problem for every f and k, giving an algorithm that runs in polynomial time and achieves an approximation error that is essentially optimal. We prove this optimal error to be 2^{- tilde Theta(k^2/n… 
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