Search scheme — where it appears
Named by 6 essays across 5 fields — each of them below, with the objects they name alongside it.
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.
The half that is never asked where
A bidirectional index is two indexes and one interval. One of them is asked for ranks several hundred times a search and for a position never — and the parts that answer "where" are two of the five it is made of.
The saving, spent
A bidirectional index whose reverse half cannot locate is a sixth smaller. Give that sixth back to the half that does locate, and the same total size answers a locate five times faster.
Every child at once
A bidirectional extension counts the occurrences of every symbol smaller than the one being added, and this collection did it with one rank per symbol — 139.7 operations an extension on a twenty-six-letter alphabet. One walk down the tree gives the same number.
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.
A factor of fourteen, for four per cent
The compound walk removes a factor of σ from every interval extension. It requires a tree whose leaves are in order, which costs between nothing and five per cent of the wavelet tree. Both numbers on one plate, and the trade is not close.
Named alongside it
The objects these essays reach for when they reach for this one.
Bidirectional indexIndex sizeRankAlphabetIntervalWavelet treeApproximate matchingBackward searchCompound operationConstant factorError budgetFilter