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Polynomial-time approximation scheme
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, in polynomial time, 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.〔Sanjeev Arora, Polynomial-time Approximation Schemes for Euclidean TSP and other Geometric Problems, Journal of the ACM 45(5) 753–782, 1998.〕
The running time of a PTAS is required to be polynomial in ''n'' for every fixed ε but can be different for different ε. Thus an algorithm running in time ''O''(''n''1/ε) or even ''O''(''n''exp(1/ε)) counts as a PTAS.
==Variants==
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