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Truly Perfect Samplers for Data Streams and Sliding Windows
[article]
2021
arXiv
pre-print
In the G-sampling problem, the goal is to output an index i of a vector f ∈ℝ^n, such that for all coordinates j ∈ [n], Pr[i=j] = (1 ±ϵ) G(f_j)/∑_k∈[n] G(f_k) + γ, where G:ℝ→ℝ_≥ 0 is some non-negative function. If ϵ = 0 and γ = 1/poly(n), the sampler is called perfect. In the data stream model, f is defined implicitly by a sequence of updates to its coordinates, and the goal is to design such a sampler in small space. Jayaram and Woodruff (FOCS 2018) gave the first perfect L_p samplers in
arXiv:2108.12017v1
fatcat:urlnlecdwfam5il6mdac6b7ywa