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

Cancellation — where it appears

The share of a signed stream's traffic that its own later updates undo, which separates what went past from what is left to be asked about. It separates what went past from what is left to be asked about, and a summary reporting the second is answering a question about a smaller stream.

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

Also named here as turnstile model — the same set of essays touches all of them, so they are one junction rather than several.

Count-Min8,192 bitsCount-Sketch8,192 bitstug-of-war, F22,560 bitsGreenwald–Khanna0 bitsexponential histogram0 bitscash register+strict turnstile±general turnstile± may go negativesliding window+ expiresdeclareddeclared93% under—declareddeclareddeclared—declareddeclareddeclared—declared——————declared40,000 updates · deletion rate 0.5 · every count exact1,758 of 1,895 under

The model a bound was quoted in

Every accuracy figure in this field's first phase was measured under four unstated assumptions. Remove them one at a time and one structure loses its guarantee on 91% of queries, another's error stops falling when it is given more state, and a third has nothing to do at all.

bounds · Bound Count-Min 4×64exact184 under16 overrms 42Count-Sketch 4×64-174-8708717499 under101 overrms 13general turnstile · insertions and deletions, counts may go negative · counts exact8,192 bits each

When the stream takes it back

Count-Min's estimate is never below the truth. That is a theorem about a stream where every update adds — and allow deletions that can take a count below zero and it comes back under on 93% of queries, with nothing in the number to say so.

wrong · Sketch

Named alongside it

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

Failure modeGuaranteeHonest limitPreconditionStream modelTurnstile modelAdditive errorCost modelCount-Min sketchCount-SketchFalsificationFrequency vector

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