FA-73228 / Probabilistic sketches / Member archive

MinHash LSH banding: threshold swaps bands and rows · case 03

Operators tune b and r against a threshold that describes a different S-curve.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Input {b, r, sigs} with sigs a list of [id, signature]. Every signature must have exactly b*r components, otherwise "invalid". Band i covers components i*r .. i*r+r-1 and hashes to the key (i, band tuple). Ids sharing any band key form a candidate pair [smaller, larger], reported once, sorted. Also return the similarity threshold (1/b)^(1/r) rounded to 3 decimals.

Why this case matters

Locality-sensitive hashing prunes all-pairs similarity search; banding mistakes either flood the verifier with false candidates or silently miss near-duplicates.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
bands 0 b=3 r=2	`[[[1, 2], [1, 3], [2, 3], [3, 5]], 0.794]`	`[[[1, 2], [1, 3], [2, 3], [3, 5]], 0.577]`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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