A 4×32 Count-Min table after 40,000 items

A 4×32 Count-Min table after 40,000 items

Each cell is a counter and each row has its own hash, so a key lands in exactly one cell per row — the four ringed cells are where key 0 went. The darker a cell, the larger its count. Key 0 truly occurred 6,793 times; its four cells hold 7,315, 7,467, 7,423, 7,660, and the estimate is the smallest of them, 7,315. Every cell is the key's count plus whatever else collided there, so every cell is an overestimate and the minimum is the least bad one. The whole table is 4,096 bits against 86,265 for an exact counter.

Drawn at 700 × 272, wide on the page. Everything above is what sketch-state returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

9 essays call sketch-state. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.