Concept

Predecessor query — where it appears

Asking for the largest stored value at or below a given one, which is how a structure with sparse anchors answers a question about every position between them. Its cost is a search over the anchors rather than a walk through the data, so it does not depend on how far the queried position is from the nearest anchor.

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

A function with r pieces

Computed at every one of eight thousand positions across four texts, a function defined on the whole suffix array agrees exactly with r−1 anchors and one addition. Anchor it at the successor instead of the predecessor — one character of code — and it disagrees at 506 of 800 positions while still returning plausible numbers.

machine · Index

Every occurrence at the same price

A regular sampling has one dial and it moves two costs together — 1,495 bits at 63 LF steps an occurrence, 131,088 bits at none. A sampling at the run boundaries sits at 10,244 bits and one predecessor query, which is a point the curve reaches only at 69,649.

space · Repeat

Named alongside it

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

FM-index Locate Measurement Phi function R-index Run boundary sampling Run-length Self-index Backward search Burrows-wheeler transform Counterexample Falsification

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