Concept

Eviction — where it appears

The removal of a key from a fixed-width table to make room for one that has just arrived, and the moment at which a counting structure stops being exact. What is charged for it — a floor added to the newcomer, or a decrement applied to every survivor — is what separates two structures that behave identically under a stream.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

fades a lazy table computed382,976fades an eager table would compute3,830,256fade multiplications (log scale)11,968 evictions, each comparing all 32 counters at one instant32 counters · half-life 4 s · bursty10× fewer

The fading nobody computes

Twelve thousand arrivals into thirty-two decayed counters cost 382,976 fade multiplications. An implementation that aged every counter on every tick would have cost 3,830,256, and the ratio is exactly the mean gap between arrivals — not a coincidence, and the reason the family is deployable.

practice · Decay
010020030040021φ 382φ 7203φ 17434φ 42885φ 1012486φ 242measured 409counts chargedlevel of the foldcharged at this levelrunning total64 shards · k = 32 · hashedcharged 409 · measured 409

The floor charged at every level

A key surviving a fold of sixty-four shards is charged 2, then 8, then 20, then 43, then 88, then 248 — the floor of whatever summary it was merged against, level by level. They sum to 409, and the damage read off the merged table is 409. The model that charged sixty-three copies of the leaf floor said 222.

floors · Floor
0.60.81.01.21.41.61.84φ share 0.908φ share 0.8516φ share 0.8032φ share 0.7564φ share 0.70predicted ÷ measuredshards, mlevel floors, uncorrectedleaf floorslevel floors, correctedk = 32 · hashed · 40,000 arrivalsworst 22% against 73% and 46%

The floor a merge does not settle at

Compute a fold's level floors from the shard histograms and the prediction over-shoots by 1.73. A merged summary's floor is not the floor a summary settles at on the same arrivals — it is 0.90 of it at four shards and 0.70 at sixty-four, straight in log₂ m at a 3% residual, because merging preserves the heavy counters and never runs their eviction cascade.

wrong · Merge

Named alongside it

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

Space-savingFixed pointHeavy hitterHistogramMeasurementMerge treeMergeable summaryPartitionShardAmortisedConstant factorCurve fitting

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