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

Depth cap — where it appears

A ceiling on how many generations of copying separate a parsed character from a literal, which bounds what producing that character costs. It is bought with phrases, and at the tightest setting the term proportional to the text that a phrase index exists to remove comes back.

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

depth 0190.1%depth 19642.9%depth 24,92915.0%depth 37,00921.4%depth 48,47325.9%depth 56,24119.0%depth 63,31010.1%depth 71,2503.8%depth 84221.3%depth 91240.4%depth 10270.1%positions32,768 characters · 1172 phrasesmean 3.98

The number that would choose a cap

A depth histogram is one linear pass — 3.16 operations a character over thirty-two thousand of them — and it says the whole text sits at a mean depth of 3.98 with a worst of ten. Nobody prints it, and every choice of cap in this collection was made without it.

practice · Parse 11010³cap on the depthphrases9.8% more phrasesevery occurrence consideredthe earliest only4,096 charactersworst at cap 4

The cap an automaton cannot see

A state of a suffix automaton stands for a set of occurrences and hands back one of them. So a capped parse driven by it can ask whether the earliest occurrence is shallow enough and cannot ask whether any occurrence is — which costs up to 9.8% of the phrases, and only at the caps that bind.

bounds · Parse 11010⁴cap on the depthphrasesno capcap 165,536 characters · 16 copies26x at cap 1

What a quadratic construction was setting

A depth cap of one costs 90% of an 8,192-character text in phrases, and 86% of a 65,536-character one. The ladder's conclusions hold at thirty-two times the size — and the number the ladder could not reach, the deepest chain a real collection produces, turns out to be fourteen.

wrong · Parse

Named alongside it

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

Lempel zivMeasurementPhraseSuffix automatonTrade offConstructionExtractionParseRepetitionDefinitionEndposGreedy

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