Examples of using Approximation algorithm in English and their translations into Portuguese
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There are numerous approximation algorithms for this problem.
Approximation algorithms for the facility location problem, BP. IC.
This is a straightforward greedy approximation algorithm.
Not all approximation algorithms are suitable for all practical applications.
This allows several results about the hardness of approximation algorithms to be proven.
The best known approximation algorithm has the non-constant approximation ratio Olog n log log n.
The best known approximation ratio of a polynomial time approximation algorithm for pathwidth is O(log n)3/2.
For example, an approximation algorithm with an approximation factor of formula_20 is known.
However, for any constant ε>0 there is a polynomial-time(4/3+ ε)-approximation algorithm for 3-dimensional matching.
It has efficient approximation algorithms, but is NP-hard to solve exactly.
In 2010, Sanjeev Arora, Boaz Barak and David Steurer found a subexponential time approximation algorithm for the unique games problem.
An approximation algorithm with finite approximation factor has to differentiate between these two cases.
No better constant-factor approximation algorithm than the above one is known.
Some of Enflo's research has been important also in other mathematical fields, such as number theory, and in computer science,especially computer algebra and approximation algorithms.
More involved techniques show that there are approximation algorithms with a slightly better approximation factor.
An approximation algorithm is called a formula_1-approximation algorithm for input size formula_2 if it can be proven that the solution that the algorithm finds is at most a multiplicative factor of formula_1 times worse than the optimal solution.
That is, unless P=NP,there is no polynomial-time(factor) approximation algorithm which does essentially better than a random partition.
Such problems arise in approximation algorithms; a famous example is the directed Steiner tree problem,for which there is a quasi-polynomial time approximation algorithm achieving an approximation factor of O( log 3 n){\displaystyle O(\log^{3}n)}(n being the number of vertices), but showing the existence of such a polynomial time algorithm is an open problem.
Thus, it is evident that(k,1)-balanced partitioning problem has no polynomial time approximation algorithm with finite approximation factor unless P NP.
In the field of approximation algorithms, algorithms are designed to find near-optimal solutions to hard problems.
The integrality gap of this ILP is 2{\displaystyle 2},so its relaxation gives a factor- 2{\displaystyle 2} approximation algorithm for the minimum vertex cover problem.
Thus, every polynomial-time approximation algorithm achieves an approximation ratio strictly less than one.
Gap reductions can be used to demonstrate inapproximability results, as if a problem may be approximated to a better factor than the size of gap,then the approximation algorithm can be used to solve the corresponding gap problem.
Approximation==The best polynomial time approximation algorithm known for this case achieves only a very weak approximation ratio, formula_1.
By using this algorithm when the clique number of a given input graph is between n/log n and n/log3n, switching to a different algorithm of Boppana& Halldórsson(1992) for graphs with higher clique numbers, and choosing a two-vertex clique if both algorithms fail to find anything,Feige provides an approximation algorithm that finds a clique with a number of vertices within a factor of O(n(log log n)2/log3n) of the maximum.
Regarding the existence of approximation algorithms, Simon(1990) proved that the problem cannot be approximated well assuming P≠ NP.
For instance, Trevisan et al. provide an optimal gadget for reducing 3-SAT to a weighted variant of 2-SAT(consisting of seven weighted 2-SAT clauses) that is stronger than the one by Garey, Johnson& Stockmeyer(1976); using it,together with known semidefinite programming approximation algorithms for MAX 2-SAT, they provide an approximation algorithm for MAX 3-SAT with approximation ratio 0.801, better than previously known algorithms. .
An ϵ-term may appear when an approximation algorithm introduces a multiplicative error and a constant error while the minimum optimum of instances of size"n" goes to infinity as"n" does.
We present several results of alon and naor(2006)that provide approximation algorithms to estimate the cutting standard matrices and for" witnesses" to the relevant quotas.
An approximation algorithm has an"absolute performance guarantee" or"bounded error""c", if it has been proven for every instance"x" that: formula_2Similarly, the"performance guarantee","R"("x, y"), of a solution"y" to an instance"x" is defined as: formula_3where"f"("y") is the value/cost of the solution"y" for the instance"x.