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

Compression schedule — where it appears

The rule deciding when a summary does its housekeeping, stated as a number of updates rather than as a property of the data. It fixes the peak state and the total housekeeping work and not the promise, so a structure that ties it to its error parameter is holding one bill constant at the cost of another.

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

ε = 0.0515 → 29 (1.93×)ε = 0.0238 → 73 (1.92×)ε = 0.0177 → 136 (1.77×)ε = 0.005152 → 270 (1.78×)ε = 0.002397 → 674 (1.70×)reportedoccupied at the peak20,000 arrivals · lognormalpeak = resident + period, to 14%

The tuples a summary does not report

A Greenwald–Khanna summary at ε = 0.01 answers `tuples` with seventy-seven. Watched through the run it holds a hundred and thirty-six. The gap is the compression period, it is 1.70 to 1.93 times across every tolerance measured, and it is the number a deployment has to allocate.

space · Space 10010³10⁴10⁵10⁶⌊1/2ε⌋ = 50151025501002005001,000tuples, and tuples examinedcompression period, in updatestuples examinedpeak tuplesresident tuplesworst rank errorε = 0.01 · 20,000 arrivalspeak 10× · work 72× · answer 1.21×

The period that is not a promise

Greenwald–Khanna's ε appears twice — once as the rank tolerance the structure promises, and once as ⌊1/2ε⌋, the number of updates between compressions. Unhook the second from the first and sweep it across a thousand-fold range. The tuples held move by 10%, the worst rank error by 21%, the peak by ten times and the housekeeping by seventy.

streaming · Rank 1 — no differencethe whole array reviewed1.03×only this batch reviewed1.22×a block window, which does alias1.48×20,000 arrivals · period 50 · cyclethe instrument reads 1.48 where an alias is known to be

The sampler that cannot alias

A block window's boundary fires on an arrival count, and a stream whose burst repeats every sixty-four arrivals is reported as perfectly even by a block of five hundred and twelve. A quantile summary compresses on an update count, which is the same arrangement. Swept against three periodic value processes and their shuffles, it does not alias — and the reason is one line of arithmetic rather than a lucky sweep.

wrong · Window

Named alongside it

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

Greenwald–KhannaMeasurementQuantile summaryPeak spaceStreaming modelTrade offAliasingAllocatorAmortised analysisArrival processAuxiliary spaceBurstiness

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