Exponential histogram — where it appears
Named by 6 essays across 4 fields — each of them below, with the objects they name alongside it.
What a window costs in bits
The approximate structure grows like the square of a logarithm and the exact one grows like the window, so the approximation wins eventually. Eventually is a window of 6,000 at a 2% tolerance — and below it the summary is larger than the thing it is summarising.
The summary that has to forget
Every structure in this field so far accumulates. Ask instead for the count over only the last thousand arrivals and no counter will do, because a counter has no record of which of its increments are old — and the repair is a row of buckets whose whole error is the oldest one.
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.
The floor under a window
An exact count of the ones in the last W arrivals needs W bits, and the argument is a pigeonhole that can be performed rather than quoted — 1,024 windows, an eight-bit state, the colliding pair produced, and the two answers it cannot tell apart.
The window that is even in the wrong currency
A window of four thousand arrivals in eight blocks retires a block every 5.1 seconds on a steady stream and anywhere between 0.57 and 14.8 seconds on a stream whose rate moves. The structure cannot tell, because it is counting arrivals, and the alert written against it is in seconds.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
ExpirySliding windowMeasurementState bitsTrade offHonest limitStream modelAliasingArrival processBurstinessClock resolutionGuarantee