Concept

Load balancing — where it appears

Assigning arriving work to one of many resources so that no resource ends up far busier than the rest. The quantity that matters is the busiest resource rather than the average, which is why schemes offering a small choice of destinations help so much.

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

024681,0244,09616,38465,536262,144keys, into as many bucketskeys in the busiest bucketone hashtwo hashes, take the emptierthree hasheslog n / log log nthe average load is 1 at every pointa lookup examines every choice, so two hashes is two probes

The second choice

Two hundred and sixty thousand keys into as many buckets. Under one hash the busiest bucket holds eight; under two, with each key going to whichever of its two is emptier, it holds four. The mean is exactly one in both. Nothing is rearranged afterwards, no key is ever moved, and the whole of the improvement is in a decision taken once, at the moment the key arrives.

randomness · Randomness
2 halves, ties go left2 choices, ties at randomone choiceload 2 or more14,61015,03717,363load 3 or more2675785,250load 4 or morenone11,236load 5 or morenonenone223load 6 or morenonenone36load 7 or morenonenone2load 8 or morenonenone165,536 keys and buckets, seededbar length is log(1 + count)

The tie that breaks left

Two choices per key, the emptier bucket wins, and when the two are equally full a coin decides. Replace the coin with a rule — split the table into halves and always send a tie to the left one — and on a million keys the buckets holding three or more fall from 9,316 to 4,694, and the busiest bucket drops from four to three. The hashing, the probes and the keys are unchanged, and the rule spends no randomness at all.

randomness · Randomness
8121620240.000010.00010.0010.01bits a keyfalse-positive ratethe whole filterone block of 512 bitsthe emptier of two 512-bit blocksone block of 1,024 bits2,048 keys · 24 filters a pointdashed: no blocks

Two blocks and the chances they add

Send each key to the emptier of two 512-bit blocks and the busiest block of a filter at sixteen bits a key holds 38 keys instead of 55. The false-positive rate does not move: 0.100% against 0.095%. At eight bits a key it doubles. A lookup cannot tell which block a key went to, so it has to ask both, and asking twice is two chances to be wrong. The repair that tames a hash table's worst bucket buys a filter nothing that a block twice as wide does not.

randomness · Randomness

Named alongside it

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

Maximum loadTwo choicesBucket loadConcentrationHash functionMeasured countRandomised data structureTail behaviourTrade offBalls in binsBlocked filterBloom filter

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