FA-73087 / Probabilistic sketches / Member archive

Count sketch frequency estimation: update omits the row sign · case 02

Colliding keys accumulate instead of cancelling, and queries multiply unsigned cells by a sign.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Input {w, d, stream, queries}; stream entries are [key, signed count]. Row r uses bucket ((A_r key + B_r) mod 2^31-1) mod w and sign +1 when ((C_r key + D_r) mod 2^31-1) is odd, else -1, from an independent hash. Updates add sign*count. A query returns the median over rows of sign*cell; for even d the median is the mean of the two middle values. Negative estimates are returned unchanged (turnstile streams).

Why this case matters

Count sketches estimate signed frequencies in turnstile streams (inserts and deletes); their unbiasedness depends on independent signs and a median across rows.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
stream 0 w=4 d=3	`[12, -2, 2, 2, -3, 0]`	`[15, 4, 3, 2, -3, 0]`	Failed

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