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

Definition — where it appears

A statement of what a quantity is, which is not a statement of how to compute it. Evaluating one directly costs whatever quantifying over everything costs, and this collection has three cases where that cost was measured and published as a property of the thing defined.

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

101001,00010010³10⁴10⁵total length of the pattern setprimitive stepsthe definitionfrom the linksthe published rulefour symbols · m = 1085.60x apart at 128 patterns

The table the links already knew

The exact good-suffix rule costs 757,058 character comparisons to build from its definition at 128 patterns, and 3,824 from the trie's failure links. Same table, checked at every node — a factor of 198, and the definition was never the algorithm.

text · Symbol 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 1,00010⁴10⁵10⁶charactersoperationscharacter comparisonstransitions and linksrepetitive · 8 copies346 phrases at 8,192

The parse in one pass of the text

The same parse, phrase for phrase, from 1,324,336 character comparisons or from 25,420 transitions and suffix-link steps. One of those numbers grows with the text and the other grows with its square, and the difference is why every measurement about a depth cap here was taken on a few thousand characters.

text · Parse 101001,00010100total length of the pattern settimes the published rule's precomputationwritten as a definitionbuilt from the linksthe published rulefour symbols · m = 10137x becomes 1.60x

The ratio that was an implementation

This collection published a factor of forty-two between two shift rules' preprocessing. Sixty-nine per cent of the denominator was a table the published rule never reads, and the numerator was a definition rather than a construction. The corrected ratio is 1.6.

wrong · Symbol

Named alongside it

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

ConstructionMeasurementBad-character ruleCommentz-walterGood-suffix ruleLempel zivParsePhrasePreprocessingShift ruleSuffix automatonTrade off

All concepts