Concept

Approximation — where it appears

A quantity computed in place of an exact one because the exact one costs too much, together with a guarantee about the direction of the difference. A safe approximation may fall short of the exact answer and may never exceed it, and how far short it falls is a measurement rather than a property of the guarantee.

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

A table wider than its input

The knapsack table has (n+1)(W+1) cells and is called polynomial. Adding one character to the input doubles it — across four settings the table grows sixty-four times while the input it is written from grows by half.

wrong · Bound

What the approximation gives up

Compared at every one of the 3,736 decisions a search could ask about, the published shift rules and the exact ones agree at all of them on a set of 128 patterns. At two patterns they differ at five of 84, by up to four positions — and the run reads 6.3% more characters.

wrong · Symbol

Named alongside it

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

Alphabet size Bad-character rule Commentz-walter Complexity class Cost model Dynamic programming Encoding Failure link Falsification Good-suffix rule Knapsack Lower bound

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