Algorithms & Data Structures
the bound is a claim, and it is checkable
Concept

Geometric series — where it appears

A sum whose terms shrink or grow by a constant ratio, such as one plus a half plus a quarter. When the ratio is below one the sum is bounded by the first term divided by one minus the ratio, which is how a stack of tightening filters keeps a fixed bound on its error.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

—execution—intention0123456789112345667822234567773333455678434345667854444567776555555678766666656787777776569888888765one unit = one subproblem given a value110 cells for one divide step, 30 held

The alignment that fits in one line

Compute the table twice and hold three rows of it. The factor of two is a geometric series and is predicted exactly; measured, it comes down from 2.269 to 2.052 as the strings grow, and the peak is 3(m+1) cells on the nose.

space · Distance 0.01%0.1%1%10%100%1,0002,0003,0004,0005,0006,0007,0008,000keys insertedabsent keys answered yesone filterm = 19,171, k = 7; dotted: the design sizedashed: the design rate

A filter past its design size

A Bloom filter sized for two thousand keys at one per cent answers yes to 15.6% of absent keys at four thousand and 68.1% at eight thousand. Nothing fails and nothing warns. A stack of filters that adds a tighter layer whenever the top one fills holds 2.0% at eight thousand, under a bound it can state in advance — in 2.9 times the bits of one filter sized for eight thousand from the start.

randomness · Randomness

Named alongside it

The objects these essays reach for when they reach for this one.

Trade offAlignmentAmortisedAuxiliary spaceBloom filterCall stackDivide and conquerDynamic programmingEdit distanceError budgetFalse-positive rateGrowth factor

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