Algorithms & Data Structures
the bound is a claim, and it is checkable
Concept

Filter — where it appears

A cheap stage that proposes candidates for an expensive one to verify. It is worth having exactly when the candidates are few, and that fraction — its selectivity — decides everything about it and appears in no statement of any of these algorithms.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

right to left8302.74xleft to right8772.89xone per piece4471.48xthe scheme3031.00xinterval extensionsall four found the same 6 positions15 characters · k = 22.74x apart

The search that starts in the middle

The same pattern, the same six occurrences, the same index — and 830 interval extensions, or 303, according to which end the search begins at. A pattern cut into three pieces has an error-free one, and only a search with two ends can start there.

text · Distance errors, by piecetaken by(0, 0, 0)1(0, 0, 1)1(0, 0, 2)1(0, 1, 0)1(0, 1, 1)1(0, 2, 0)3(1, 0, 0)2(1, 0, 1)2(1, 1, 0)3(2, 0, 0)30 of 10 covered more than once · the numbers are the searchesk = 2 · 3 pieces10 distributions

A schedule nobody writes down

A search scheme is valid when its searches between them cover every way the errors can fall — ten cases at two errors, enumerable in a line. A scheme missing one of them finds seven occurrences of eight, all real, at the right error counts, and reports nothing wrong.

wrong · Distance

Named alongside it

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

Approximate matchingBidirectional indexError budgetMeasurementPigeonholeSearch schemeTrade offAlphabetBacktrackingConstant factorCoveringFalse negative

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