What are approximation algorithms explain them using a suitable example?
A simple example of an approximation algorithm is one for the minimum vertex cover problem, where the goal is to choose the smallest set of vertices such that every edge in the input graph contains at least one chosen vertex.
Why approximation algorithms are used to solve NP-hard problem what do you mean by polynomial time approximation algorithm?
An Approximate Algorithm is a way of approach NP-COMPLETENESS for the optimization problem. This technique does not guarantee the best solution. The goal of an approximation algorithm is to come as close as possible to the optimum value in a reasonable amount of time which is at the most polynomial time.
Why do we need approximation algorithm?
Approximation algorithms are typically used when finding an optimal solution is intractable, but can also be used in some situations where a near-optimal solution can be found quickly and an exact solution is not needed. Many problems that are NP-hard are also non-approximable assuming P≠NP.
What is an example of an approximation algorithm?
A simple example of an approximation algorithm is one for the minimum vertex cover problem, where the goal is to choose the smallest set of vertices such that every edge in the input graph contains at least one chosen vertex.
Why is there a 2-approximation algorithm for relaxation?
Since the value of the relaxation is never larger than the size of the optimal vertex cover, this yields another 2-approximation algorithm.
What is the guarantee of algorithms?
In an overwhelming majority of the cases, the guarantee of such algorithms is a multiplicative one expressed as an approximation ratio or approximation factor i.e., the optimal solution is always guaranteed to be within a (predetermined) multiplicative factor of the returned solution.
What is the approximation ratio of the maximization problem?
In the literature, an approximation ratio for a maximization (minimization) problem of c – ϵ (min: c + ϵ) means that the algorithm has an approximation ratio of c ∓ ϵ for arbitrary ϵ > 0 but that the ratio has not (or cannot) be shown for ϵ = 0.