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A Bloom filter is a space-efficient data structure used for probabilistic set membership testing. When testing an object for set membership, a Bloom filter may give a false positive. The analysis of the false positive rate is a key to understanding the Bloom filter and applications that use it. The authors show experimentally that the classic analysis for false positive rate is wrong. They formally derive a correct formula using a balls-and-bins model and show how to numerically compute the new, correct formula in a stable manner. They also prove that the new formula always results in a predicted greater false positive rate than the classic formula.
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