Approximation algorithms

class of algorithms that find approximate solutions to optimization problems

(as a form of proximity search (metric space)) optimization problem of finding the point in a given set that is closest (or most similar) to a given point

algorithm that approximates solutions to the travellng salesman problem on a metric space, guaranteeing that its solutions will be within 1½ of the optimal solution length; discovered by Nicos Christofides in 1976

classical problem in combinatorics

used to determine solution to travelling salesman problem

complexity class

In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short). In simple terms, problems in this class have efficient algorithms that can find an answer within some fixed multiplicative factor of the optimal answer.

In computer science, particularly the study of approximation algorithms, an L-reduction ("linear reduction") is a transformation of optimization problems which linearly preserves approximability features; it is one type of approximation-preserving reduction. L-reductions in studies of approximability of optimization problems play a similar role to that of polynomial reductions in the studies of computational complexity of decision problems.