Concept

Reverse index — where it appears

An index built over a text read backwards, which turns a leftward extension into a rightward one. A bounded-error index walk needs one to compute a lower bound on the errors its remaining pattern must cost, and it is the same size as the index it prunes — so the structure doubles.

Named by 5 essays across 4 fields — each of them below, with the objects they name alongside it.

atgaattcatgagtgacaag00000111111112222222errorsthe pattern, left to right · D belowleast errors neededD, the bound4 symbols · m = 2090 ranks · 2 resets

The errors the rest of the pattern needs

Read the pattern left to right in an index of the reversed text and count the points where the interval empties. That count is a lower bound on the errors any alignment of the prefix must contain, it costs 72 rank operations, and it removes 70% of a search tree.

text · Distance
1234567characters addedoccurrencesgrown leftwardsgrown rightwards"tgatatt"4,000 characters · four symbols1 occurrences

An interval that grows at both ends

A backward search step is two ranks. A bidirectional step is two ranks and the width of the interval for every symbol that sorts before the one being added — 16.5 ranks on four symbols and 138.6 on twenty-six, which is a cost no account of the structure mentions.

indexes · Distance
ranks to compute D72extensions removed27,906extensions remaining12,051one search · k = 3 · 4,000 charactersand one more index: 17,033 bits4,000 characters · m = 16388 extensions a rank

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.

space · Distance
one index35,3354.31 bits/charthe forward half35,3354.31 bits/charthe reverse half35,3354.31 bits/charboth, which is the structure70,6708.63 bits/charbits8,192 characters · sample 322.00x one index

The structure that was supposed to halve

A bidirectional index holds the transform of the text and the transform of its reversal — 35,335 bits each, 70,670 together, exactly twice one index. The deferral that named it hoped it would stop the index doubling. It does not remove the doubling; it reuses it.

space · Distance
atgaattcatgagtgacaag00000111111112222222errorsthe pattern, left to right · D belowleast errors neededD, the bound4 symbols · m = 2090 ranks · 2 resets

The pruning that loses an occurrence

Two versions of the same lower-bound pruning, each one character away from correct. Both return only real occurrences, both return fewer of them, and no check that asks whether the answers are right can tell either from the truth.

wrong · Distance

Named alongside it

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

MeasurementFM-indexBacktracking searchBackward searchError budgetIndex sizeLower boundPruningTrade offApproximate matchingBidirectional indexConstant factor

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