Shared prefix — where it appears
Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.
The comparison that is not one comparison
Sorting 512 keys costs 3,955 comparisons whatever the keys are, and between 7,849 and 134,409 character examinations depending only on how much those keys have in common. The first number is the one every bound so far is stated in. The second is the one the machine pays, it grows without limit, and nothing here has ever counted it.
The columns the candidates share
Three thousand tables against one query, and most of them begin the same way. Stored as a trie, the 2,424-word vocabulary has 7,710 distinct prefixes holding 17,239 letters, and a search that computes one column per prefix reads 61,449 cells against 156,714 — before it applies any bound at all. Apply the bound at a prefix instead of at a word and it reads 16,958, beating a list search that was told the answer in advance.
A trie fitted to its queries
A nearest-word search over a trie of 2,424 words gives a column to about 30% of the prefixes each query, and it was proposed that a stream of queries would pick out a part of the trie worth keeping and a part worth collapsing. A hundred queries have visited 93% of it; two thousand, 99.5%. A stream does not choose a part of the trie. It chooses a distance: misspelt vocabulary words all lie within two edits, and a search that starts at the median past answer does a fifth of the work of one that discovers its bound. Misspellings of words the vocabulary lacks break that, unless the search tries the learned bound once and then gives it up.
Named alongside it
The objects these essays reach for when they reach for this one.
CorpusDynamic programmingEdit distanceLower boundMeasured countOutput-sensitivePruningSubproblemTrieCharacter comparisonComparison sortCost model