Lower bounds on frequency estimation of data streams
نویسنده
چکیده
We consider a basic problem in the general data streaming model, namely, to estimate a vector f ∈ Z that is arbitrarily updated (i.e., incremented or decremented) coordinatewise. The estimate f̂ ∈ Z must satisfy ‖f̂ − f‖∞ ≤ ǫ‖f‖1, that is, ∀i (|f̂i − fi| ≤ ǫ‖f‖1). It is known to have Õ(ǫ) randomized space upper bound [6], Ω(ǫ log(ǫn)) space lower bound [4] and deterministic space upper bound of Ω̃(ǫ) bits. We show that any deterministic algorithm for this problem requires space Ω(ǫ−2(log‖f‖1)(logn)(log (ǫ)) bits.
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We consider a basic problem in the general data streaming model, namely, to estimate a vector f ∈ Z that is arbitrarily updated (i.e., incremented or decremented) coordinatewise. The estimate f̂ ∈ Z must satisfy ‖f̂ − f‖∞ ≤ ‖f‖1, that is, ∀i (|f̂i − fi| ≤ ‖f‖1). It is known to have Õ( −1) randomized space upper bound [4], Ω( −1 log( n)) space lower bound [2] and deterministic space upper bound of ...
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