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

Stabbing query — where it appears

Asking which of a set of intervals contain a given point. It is a range query with two of its sides at infinity, and it is the shape of the question a phrase index asks when it propagates an occurrence into every phrase that copied from a region holding it.

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

rank among the boundaries, sorted by the text before themsorted by the text after0 in the rectanglepattern "ss is un"split after 40 end with the left half0 begin with the rightEnglish-like · 2 copies of 512z = 156 · 0 crossing

The candidates a filter cannot avoid

A phrase index answers a search by intersecting two ranges of boundaries, and it does the intersection by walking the smaller one. On a collection of thirty-two copies that is 4,355 phrase examinations to produce 32 occurrences — 136 examinations each, and rising.

indexes · Grid rank among the boundaries, sorted by the text before themsorted by the text after0 in the rectanglepattern "ss is un"split after 40 end with the left half0 begin with the rightEnglish-like · 2 copies of 512z = 156 · 0 crossing

A rectangle over a permutation

Two orderings of one set of boundaries are two permutations, so a phrase index's intersection is a rectangle over a permutation grid — the one point set a wavelet tree stores exactly, at one bit per point per level and no coordinates at all.

structures · Grid

Named alongside it

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

GridOutput-sensitivePrimary occurrenceRange reportingSecondary occurrenceSelf-indexBit vectorConstructionIndex sizeLempel ziv parseLocateMeasurement

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