Universal Sketches for the Frequency Negative Moments and Other Decreasing Streaming Sums
- Braverman, Vladimir
- Chestnut, Stephen R.
DOIAbstract
Given a stream with frequency vector f in n dimensions, we characterize the space necessary for approximating the frequency negative moments Fp, where p<0, in terms of n, the accuracy, and the L_1 length of the vector f. To accomplish this, we actually prove a much more general result. Given any nonnegative and nonincreasing function g, we characterize the space necessary for any streaming algorithm that outputs a (1 +/- eps)-approximation to the sum of the coordinates of the vector f transformed by g. The storage required is expressed in the form of the solution to a relatively simple nonlinear optimization problem, and the algorithm is universal for (1 +/- eps)-approximations to any such sum where the applied function is nonnegative, noni...
Add to ORKG