Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Transcribed Image Text:You are given an insertion-only stream, only consisting of (add, i) updates where i e {1,...,n}.
There are m such updates. Suppose you want to sample a random insertion in the stream.
For example, if the insertions formed the sequence (1,3, 5, 5, 7, 1, 5) with m = 7, then the goal
is to output 1 with probability 2/7, 3 with probability 1/7, 5 with probability 3/7, and 7 with
probability 1/7.
Consider the following algorithm that acts as follows on the t'th insertion. If t = 1, let X be
the first inserted element. For t > 1, with probability 1/t, let X be the tth inserted element
and with probability 1– 1/t, don't change X. At the end of the stream, return X.
Show that X is indeed uniformly sampled from the m insertions.
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