## What is approximation algorithm example?

## What is approximation algorithm 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.

**What is a 3 approximation algorithm?**

A 3-approximation to minimum vertex cover in a bounded- degree graph can be found by a deterministic local algorithm in 2∆ + 1 com- munication rounds, where ∆ is the maximum degree of the graph. The algo- rithm does not need unique node identifiers; port numbering is sufficient.

### What are the types of approximation algorithms?

Types of approximation algorithms. Fully polynomial-time approximation scheme. Constant factor. Knapsack problem.

**What is a two approximation algorithm?**

An algorithm with approximation ratio k is called a k-approximation algorithm; both algorithms above would be called 2-approximation algorithms. When the approximation ratio is close to 1, it is often more useful to look at the approximation error, which is defined as the approximation ratio minus 1.

## How approximation algorithm is selected?

If an algorithm reaches an approximation ratio of P(n), then we call it a P(n)-approximation algorithm. For a maximization problem, 0< C < C*, and the ratio of C*/C gives the factor by which the cost of an optimal solution is larger than the cost of the approximate algorithm.

**Which one is better approximation algorithm?**

Therefore, a 1-approximation algorithm gives an optimal solution. Some problems have polynomial-time approximation algorithm with small constant approximate ratios, while others have best-known polynomial time approximation algorithms whose approximate ratios grow with n.

### What is K approximation algorithm?

In computer science, k-approximation of k-hitting set is an approximation algorithm for weighted hitting set. The input is a collection S of subsets of some universe T and a mapping W from T to non-negative numbers called the weights of the elements of T.

**What is C approximation algorithm?**

We say that A is a c-approximation for P if for every input x of P: OPT(x) ≤ A(x) ≤ c · OPT(x) 2. If P is a maximization problem. We say that A is a c-approximation for P if for every input x of P: OPT(x) c ≤ A(x) ≤ OPT(x) In both cases, we call c the approximation ratio of A.