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

Bitmap — where it appears

One bit per member of a small universe, used as a set. Its cost is the universe rather than the set, so what matters is how it is cleared: sweeping it costs the universe per query, and unsetting exactly what was set costs the answer.

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

range consideredminimum atC[at] < lonew document[476, 489)483 · document 4yesyes[476, 483)477 · document 1yesyes[476, 477)476 · document 0yesyes[478, 483)482 · document 2yesyes[478, 482)478 · document 0nono[484, 489)486 · document 3yesyes[484, 486)484 · document 0nono[487, 489)487 · document 2nono8 steps, 5 documents, and the two columns never differrows 476–489 · 8 documents8 steps

A document already in the answer

The same walk, with the chain's test replaced by a lookup in the answer so far. It reports the same documents at the same cost, and two exchanged lines make it lose nine of seventeen without failing.

structures · Index tree · suffix array2,363,886tree · text656,635tree · document array1,050,616tree · previous-occurrence chain2,363,886tree · range minimum4,727,772succinct · suffix array2,363,886succinct · text656,635succinct · document array1,050,616succinct · previous-occurrence chain2,363,886succinct · range minimum1,483,854chainless · suffix array2,363,886chainless · text656,635chainless · document array1,050,616chainless · range minimum1,483,854chainless · reported bitmap256131,327 characters · 256 documents6 parts

What the chain cost

The chain of previous occurrences is one row number per row — exactly as wide as the suffix array it sits beside, and the largest single part of a document-listing apparatus. It is now absent, and what replaces it is one bit per document.

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Named alongside it

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

Document arrayDocument listingIndex sizePrevious occurrence chainRange minimumCheckDocument collectionInvariantOutput-sensitiveOverheadRecursionSpace

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