Concept

Phi function — where it appears

The map sending a text position to the position that precedes it in suffix order. It is linear with slope one between consecutive positions whose rows begin a run, so r anchors and one addition answer it everywhere, and applying it repeatedly turns one known occurrence into all of them.

Named by 3 essays across 3 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

The occurrence carried through the search

Backward search returns how many and not where, and every index on this site pays for the second question separately. Carrying one occurrence along with the interval costs a lookup on 75% of the steps for a two-character pattern and on 18% of them for a sixteen-character one, and it is what makes a run-boundary sampling usable at all.

indexes · 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 R-index Run boundary sampling Run-length Self-index Backward search Burrows-wheeler transform Index size Predecessor query Sampling

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