What does APX stand for?
What does APX mean? This page is about the various possible meanings of the acronym, abbreviation or slang term: APX.
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What does APX mean?
- In complexity theory the class APX is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant. In simple terms, problems in this class have efficient algorithms that can find an answer within some fixed percentage of the optimal answer. For example, there is a polynomial-time algorithm which will find a solution to the bin packing problem that uses at most 5% more than the smallest possible number of bins. An approximation algorithm is called a c-approximation algorithm for some constant c if it can be proven that the solution that the algorithm finds is at most c times worse than the optimal solution. Here, c is called the approximation ratio. Depending on whether the problem is a minimization or a maximization problem, this can either denote c times larger or c times smaller, respectively. For example, the vertex cover problem and traveling salesman problem with triangle inequality each have simple 2-approximation algorithms. In contrast, it's proven that the traveling salesman problem with arbitrary edge-lengths can not be approximated with approximation ratio bounded by a constant as long as the Hamiltonian-path problem can not be solved in polynomial time, that is unless P = NP.