Concept

Parametric search — where it appears

Treating an optimisation's parameter as a variable and asking how the optimum changes as it moves. It turns a ratio objective into a sequence of ordinary ones, and for alignment it divides the parameter plane into a few regions that share one optimal answer.

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

A distance divided by a length is not a rate

Two substitutions turn "ab" into "ba", a distance of two over an alignment of two columns — a rate of 1.00. Deleting, matching and inserting also costs two, over three columns, for 0.67. Both are alignments of the same pair, the second has the better rate, and the optimal alignment is not the one that achieves it. Over every pair of strings up to three characters on three letters, 21% disagree.

tables · Cost

The parameter plane has few answers

Sweep the cost of opening a gap against the cost of extending one over five hundred and seventy-six settings, and the optimal alignment of intention against execution takes four values — one of them at 571 of the settings. Under a linear model the plane divides into three wedges through the origin, because doubling every cost changes nothing and only the ratio is a parameter. Tuning an aligner is choosing a region, and most of the plane is one.

tables · Cost

Named alongside it

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

Alignment Cost model Dynamic programming Edit distance Affine gap Denominator Honest limit Measured count Metric Normalisation Optimality Optimisation

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