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Copy file name to clipboardExpand all lines: lsm-tree.cabal
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Querying a Bloom filter returns either \"maybe\" meaning the key is possibly in the run or \"no\" meaning the key is definitely not in the run.
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When a query returns \"maybe\" while the key is /not/ in the run, this is referred to as a /false positive/.
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While the database executes a lookup operation, any Bloom filter query that returns a false positive causes the database to unnecessarily read a run from disk.
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The probabliliy of these spurious reads follow a [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) \(\operatorname{Binomial}(r,\operatorname{FPR})\)
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where \(r\) refers to the number of runs and \(\operatorname{FPR}\) refers to the false-positive rate of the Bloom filters.
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Hence, the expected number of spurious reads for each lookup operation is \(r\cdot\operatorname{FPR}\).
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The probabliliy of these spurious reads follow a [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) \(\text{Binomial}(r,\text{FPR})\)
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where \(r\) refers to the number of runs and \(\text{FPR}\) refers to the false-positive rate of the Bloom filters.
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Hence, the expected number of spurious reads for each lookup operation is \(r\cdot\text{FPR}\).
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The number of runs \(r\) is proportional to the number of physical entries in the table. Its exact value depends on the merge policy of the table:
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[@LazyLevelling@]
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The value must be in the range \((0, 1)\).
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The recommended range is \([1\mathrm{e}{ -5 },1\mathrm{e}{ -2 }]\).
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The total in-memory size of all Bloom filters scales /linearly/ with the number of physical entries in the table and is determined by the number of physical entries multiplied by the number of bits per physical entry, i.e, \(n\cdot\operatorname{BPE}\).
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The total in-memory size of all Bloom filters scales /linearly/ with the number of physical entries in the table and is determined by the number of physical entries multiplied by the number of bits per physical entry, i.e, \(n\cdot\text{BPE}\).
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Let us consider a table with 100 million physical entries which uses the default table configuration for every parameter other than the Bloom filter size.
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