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

Commensurability — where it appears

Whether a structure's housekeeping interval divides, or is divided by, a period in the data it is summarising. Where the two are commensurate the housekeeping meets the same phase of the cycle every time, which is the condition under which a boundary that discards arrivals reports a periodic stream as an even one.

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

1.821251.951.431752.731.302253.521.292503.911.183755.861.005128.00longest block ÷ shortestarrivals per block, and bursts per blockpart of a bursta whole numberbursts of 64 · 8 blocks · 20,000 arrivalsdispersion 0.57 and a ratio of 1.00

The boundary that hides the burst

A window whose blocks hold five hundred and twelve arrivals reports a perfectly even stream — every block the same duration to the tick — while the arrivals it is retiring have an index of dispersion of 0.57. Move the block to a hundred and twenty-five and the same stream varies by 1.8 times.

wrong · Window 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.

AliasingArrival processBurstinessFailure modeMeasurementSamplingSliding windowTemporal resolutionClock resolutionCompression scheduleCounterexampleExpiry

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