Concept

Seeded randomness — where it appears

Randomness drawn from a stated seed so a run reproduces, with the data's seed and the algorithm's kept separate because sharing them destroys independence. The data's seed and the algorithm's are kept apart, because sharing them makes an experiment about independence into an experiment about a coincidence.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

level 1level 2level 3level 4level 5key 21search: 8 comparisons, 3 hops26 keys, p = 0.5, seed 2026081057 coin flips decided the shape

A structure made of coin flips

Insert the same 512 keys into a skip list twice, once sorted and once shuffled, from the same seed, and the two structures are identical — the same 11 levels, the same height for every key, the same silhouette. Nothing about the data reached the layout. The 1,064 coin flips did all of it.

randomness · Randomness
average 8.001,0242,048bucket, 0 to 255keys in the bucketmultiply–shift · keys built for this hashworst bucket 2,048 against 8.0

The adversary who knows the seed

Every randomised figure on this site is drawn from a stated seed, so that the numbers in the captions are the numbers on the reader's screen. That is also the exact condition under which none of the guarantees those figures demonstrate applies. A published seed is a published function.

wrong · Distribution
1 coefficient13 members2 coefficients169 members3 coefficients2,197 members4 coefficients28,561 members1 key2 keys3 keys4 keys5 keysexact92% gone99% gone100% gone100% goneexactexact92% gone99% gone100% goneexactexactexact92% gone99% goneexactexactexactexact92% goneevery member walked · GF(13) · no tolerance and no seeddegree 1, 2, 3, 4

The independence an estimator spends

Every sketch's analysis begins by assuming a truly random hash, and nobody comes back to that line. Independence has a degree, the degree is enumerable over a small field, and an estimator's mean and its variance spend different amounts of it.

randomness · Moment
1101001,00010,00010⁵10⁶k, the elements the caller readscomparisonssort all, read kbuild a heap, pop kselect k, sort thoseincremental quicksortkeep the best k while scanningknockout tournamentdashed: the floorlabels at k = 1,00065,536 random distinct keysevery answer checked

The count of the part that was read

Handing back the smallest ten of 65,536 keys in order costs 965,656 comparisons by sorting them and 65,670 by a knockout tournament, against a floor of 65,526. Read to the last element, the same tournament makes exactly merge sort's 965,656 — it is merge sort, charged one element at a time. A sort's count has no term for how much of its answer anyone reads, and the two floors that do have one cannot simply be added.

counting · Count

Named alongside it

The objects these essays reach for when they reach for this one.

Adversarial inputComparison countDistributionRandomised algorithmSkip listTreapWorst caseBinary searchBinary search treeEntropyEstimatorExpected case

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