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Reservoir sampling

Reservoir sampling is a family of randomized algorithms for randomly choosing n samples from a list S containing N items, where n is either a very large or unknown number. Typically N is large enough that the list doesn’t fit into main memory. The most common example was labelled Algorithm R by Jeffrey Vitter in his paper on the subject.

This simple O(N) algorithm as described in the Dictionary of Algorithms and Data Structures consists of the following steps (assuming that the arrays are one-based, and that the number of items to select, n,  is smaller than the size of the source array, S):

array R[k];    // result

integer i, j;

// fill the reservoir array
for each i in 1 to k do
    R[i] := S[i]

// replace elements with gradually decreasing probability
for each i in k+1 to length(S) do
    j := random(1, i);   // important: inclusive range
    if j <= k then
        R[j] := S[i]
Categories: programming
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