# Grps. involved with Scholastic Book Fairs

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## Possible Answers: PTAS.

Last seen on: Universal Crossword – May 17 2022 s

### Random information on the term “PTAS”:

In computer science, a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).

A PTAS is an algorithm which takes an instance of an optimization problem and a parameter ε > 0 and produces a solution that is within a factor 1 + ε of being optimal (or 1 − ε for maximization problems). For example, for the Euclidean traveling salesman problem, a PTAS would produce a tour with length at most (1 + ε)L, with L being the length of the shortest tour.

The running time of a PTAS is required to be polynomial in the problem size for every fixed ε, but can be different for different ε. Thus an algorithm running in time O(n1/ε) or even O(nexp(1/ε)) counts as a PTAS.

A practical problem with PTAS algorithms is that the exponent of the polynomial could increase dramatically as ε shrinks, for example if the runtime is O(n(1/ε)!). One way of addressing this is to define the efficient polynomial-time approximation scheme or EPTAS, in which the running time is required to be O(nc) for a constant c independent of ε. This ensures that an increase in problem size has the same relative effect on runtime regardless of what ε is being used; however, the constant under the big-O can still depend on ε arbitrarily.