Unit of cost — where it appears
Named by 12 essays across 8 fields — each of them below, with the objects they name alongside it.
An index larger than what it indexes
A suffix array over 16,384 characters is 229,376 bits, and it cannot answer a single question without the 81,920 bits of text beside it. Nearly four times the text, to search the text. Every index on this site had been weighed at zero until somebody put one on a scale.
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.
A cost that is not one
The same eighty-one cells, filled by the same recurrence, return 6, 10, 10 and 15 — in edits, in cost, in bits and in bits again. Only the first is a count of anything, two of them are equal by arithmetic coincidence, and the alignment each one chooses is different.
A cell that has to know where it is
A gap of four characters is usually one event, not four. No recurrence over a single table can charge it that way, because the price of a gap character depends on how the cell above it was reached and a cell holding one number has thrown that away. The repair is three tables, and it costs exactly three times the cells.
The exchange rate nobody wrote down
Three earlier essays have said in passing that the ranking would change if the elements were large records. None of them computed it. Computed, selection sort goes from second-worst of seven at four bytes a record to best of seven at five hundred and twelve — and the crossover against each rival is a division that takes one line.
Rank is the only thing it does
Constant time and o(n) extra space — a phrase true of a rank directory costing 163% overhead and reading three words, and equally true of one costing 3% and reading eighteen. Both numbers are decided by two integers somebody typed into a header, and the phrase names neither.
The q-grams an error cannot destroy
A pattern of twenty-four characters holds twenty-one four-grams. Two errors can destroy at most eight of them, so any occurrence with two errors still shares thirteen — and a filter that keeps only the windows sharing thirteen proposes 104 of 3,977 and computes 16,744 table cells instead of 96,000.
The search that spends a budget
A backward search narrows one interval per pattern character. Give it a budget of three errors and it narrows 39,943 of them instead, finds every occurrence the whole table finds, and reads not one character of the text — 177,046 index ranks against 60,000 table cells and zero characters examined.
The period that is not a promise
Greenwald–Khanna's ε appears twice — once as the rank tolerance the structure promises, and once as ⌊1/2ε⌋, the number of updates between compressions. Unhook the second from the first and sweep it across a thousand-fold range. The tuples held move by 10%, the worst rank error by 21%, the peak by ten times and the housekeeping by seventy.
A bound that has to be paid for
The pruning removes seventy per cent of a search tree for seventy-two rank operations. It also needs an FM-index of the reversed text — 17,033 bits against the forward index's 17,032 — which doubles the structure whose small size was the entire argument for walking an index.
Three savings in three currencies
The same six occurrences, found four ways. The table computes 60,000 cells and reads 60,000 characters. The counting filter computes 6,251 cells and reads 13,022 characters. The seed filter computes 3,325 and reads 550. The index walk computes none, reads none, and performs 18,645 ranks.
The operations a candidate count leaves out
The grid examines 33 candidates where the scan examines 4,355 — a factor of 132. Counted in the operations each of them performs, the same query is 2,471 against 4,355, and the factor is 1.8.
Named alongside it
The objects these essays reach for when they reach for this one.
MeasurementTrade offCost modelEdit distanceHonest limitSelf-indexApproximate matchingBacktracking searchError budgetFilteringFM-indexIndex size