In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems...

time algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a...

produced with sophisticated algorithms. In addition, many approximation algorithms exist. For example, the first fit algorithm provides a fast but often...

A parameterized approximation algorithm is a type of algorithm that aims to find approximate solutions to NP-hard optimization problems in polynomial time...

An approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus...

optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids and give constant-factor approximations to optimization...

maximum. Although the approximation ratio of this algorithm is weak, it is the best known to date. The results on hardness of approximation described below...

approximation algorithm achieves an approximation ratio strictly less than one. There is a simple randomized 0.5-approximation algorithm: for each vertex...

only estimated via noisy observations. In a nutshell, stochastic approximation algorithms deal with a function of the form f ( θ ) = E ξ ⁡ [ F ( θ , ξ )...

matter of fact, the term "algorithm" was not commonly extended to approximation algorithms until later; the Christofides algorithm was initially referred...

the runtime is O(n) and the approximation ratio is at most 3/2 ("approximation ratio" means the larger sum in the algorithm output, divided by the larger...

(they are symmetric and obey the triangle inequality). It is an approximation algorithm that guarantees that its solutions will be within a factor of 3/2...

trivial algorithm attains a (d-1)-approximation algorithm for the maximum independent set. In fact, it is possible to get much better approximation ratios:...

where r is a number in (0,1) called the approximation ratio. The following very simple algorithm has an approximation ratio of 1/2: Order the inputs by descending...

A minimax approximation algorithm (or L∞ approximation or uniform approximation) is a method to find an approximation of a mathematical function that...

important tools for developing approximation algorithms for NP-hard maximization problems. The first approximation algorithm based on an SDP is due to Michel...

is an approximation algorithm for performing an N-body simulation. It is notable for having order O(n log n) compared to a direct-sum algorithm which...

state-of-the-art algorithm is due to Avidor, Berkovitch and Zwick, and its approximation ratio is 0.7968. They also give another algorithm whose approximation ratio...

polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short). In simple...

reviewed by Duan and Pettie (see Table II). Their work proposes an approximation algorithm for the assignment problem (and the more general maximum weight...

understanding its approximation hardness". The best polynomial time approximation algorithm known for this case achieves only a very weak approximation ratio, n...

Philip Wolfe in 1956. In each iteration, the Frank–Wolfe algorithm considers a linear approximation of the objective function, and moves towards a minimizer...

decades, the best known approximation to the traveling salesman problem in a metric space was the very simple Christofides algorithm which produced a path...

know quasi-polynomial time algorithms, but no polynomial time algorithm is known. Such problems arise in approximation algorithms; a famous example is the...

any algorithm for the knapsack problem into an approximation algorithm for the GAP. Using any α {\displaystyle \alpha } -approximation algorithm ALG for...

tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead....

preserve the quality of approximations to that solution. If the graph is a metric space then there is an efficient approximation algorithm that finds a Hamiltonian...

issue by trying all values of k. A simple greedy approximation algorithm that achieves an approximation factor of 2 builds C {\displaystyle {\mathcal {C}}}...

quasi-Newton methods like BFGS, is an algorithm of an iterative method or a method of successive approximation. An iterative method is called convergent...

computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems...