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

Primary occurrence — where it appears

An occurrence of a pattern that crosses at least one phrase boundary of the parse. It is the only kind an index built on a parse has to search for, because everything lying inside a single phrase is by definition a copy of something earlier.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

1,00010,00010⁴bits12481632characters in the collection · copies aboveFM-index, compressedr-indexphrase indexEnglish-like · divergence 0z 156 · r 233

An index with z in its size

Over thirty-two copies of one text, an index built on the parse is 8,892 bits, the r-index is 17,047 and the entropy-bounded index is 34,615. Over eight thousand characters of four-symbol text the same three are 7,844, 25,177 and 20,413, and the smallest of the three has changed places twice.

indexes · Parse 1,00010,000110occurrences12481632characters in the collection · copies aboveall occurrencessecondaryprimarypattern "ss is un" · z = 1561 primary · 31 secondary

The occurrences that cross a boundary

One pattern, thirty-two copies of a text, thirty-two occurrences. The search finds one of them and produces the other thirty-one by arithmetic, and the count it finds is the same one at two copies, at eight and at thirty-two — the searching does not grow when the answer does.

text · Parse 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.

Secondary occurrenceSelf-indexIndex sizeLempel ziv parseLocateMeasurementPhraseGridOutput-sensitiveR-indexRange reportingRepetition

All concepts