Summary — where it appears
Named by 8 essays across 5 fields — each of them below, with the objects they name alongside it.
The pass that was never a parameter
One pass is the streaming model's defining restriction, and this collection has enforced it by making a second read throw. A prohibition cannot be swept. Turn it into a dial and the first thing it says is that a second pass turns eighteen candidate heavy hitters, six of them wrong, into twelve that are exactly right — for 3,680 bits carried across the boundary and no extra space at all.
The bits that say when
A windowed cardinality estimator holds 4,592 bits and 2,392 of them are clocks. Every summary in this collection has reported its size from the shape of its own structure, and not one of those numbers has ever been asked what the bits were for — so the resource that half of these structures spend most of their state on has been invisible while being counted.
An error measured against the answer
A quantile summary asked for the 99.9th percentile answered 9,694 where the truth was 256, and violated nothing — its promise was a rank error under one per cent of the stream and it delivered a tenth of one per cent. One per cent of the stream is a thousand per cent of the tail, and no amount of extra state changes that.
The tuples a merge does not give back
A merge of thirty-two quantile summaries keeps seven times the tuples of one summary over the same values, and sixty-four keeps ten and a half. Fitted across the sweep the count goes as the shard number to the power 0.56, which answers what it converges to — it does not.
The count that outlives its arrivals
A Misra-Gries counter holding six thousand is not a record of six thousand arrivals. It is a number that has been added to and taken from, and nothing in the structure says when any of it happened — so when the key stops arriving the counter stays, and goes on reporting a key with nothing in the window as the heaviest thing in it.
The counter that takes the smallest slot
Space-Saving keeps two numbers per key and they bracket the truth from both sides. On the twenty heaviest keys of a stream its mean error is a tenth of one arrival, against a hundred and ten for Misra-Gries at the same bits — and on the keys ranked past a hundred the ordering reverses.
The digest that promises nothing
The t-digest is the quantile structure most widely deployed and the only one with no proven bound on its rank error at any quantile. Measured, it beats the structure that does have one — and on two clusters with a gap between them it returns 431.5, where the data holds nothing at all between 40 and 800.
A summary's silence is a bound, not a count
When both sides of a join are skewed towards the same values the textbook estimate is 399 times too low and the order it picks costs 244 times the better one; two counters a side repair it. Skew them towards different values and the same estimate becomes 254 times too high — and the counters have nothing to say, because no value is in both summaries. Using their silence instead repairs the middle of the sweep and makes the far end six times worse.
Named alongside it
The objects these essays reach for when they reach for this one.
MeasurementState bitsGuaranteeHonest limitMisra–GriesTrade offHeavy hitterGreenwald–KhannaRank errorZipfExpiryHeavy tail