What are the different types of approximation algorithm?

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

How are the approximation algorithms useful problem solving?

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.

For which condition there is no α approximation algorithm for the general Versiton of TSP for any constant α?

Lemma 9 Metric-TSP does not admit an α additive approximation algorithm for any polynomial- time computable α unless P = NP.

What is tractable problem?

Tractable problem, in computational complexity theory, a problem that can be solved in polynomial time. Tractable, ease of obtaining a mathematical solution such as a closed-form expression.

What is approximation algorithm give approximate algorithm for Travelling salesman problem?

What is the 2 approximation algorithm for TSP? When the cost function satisfies the triangle inequality, we may design an approximate algorithm for the Travelling Salesman Problem that returns a tour whose cost is never more than twice the cost of an optimal tour. The idea is to use Minimum Spanning Tree (MST).

What is approximation ratio of the approximate vertex cover problem?

Vertex Cover: We begin by showing that there is an approximation algorithm for vertex cover with a ratio bound of 2, that is, this algorithm will be guaranteed to find a vertex cover whose size is at most twice that of the optimum.

What is an absolute approximation algorithm?

– Absolute approximation algorithm is the most desirable approximation algorithm. ∗ For most NP-hard problems, fast algorithms of this type exists only if P = NP. – Example: Knapsack problem. ∗ n = 3, m = 100, P = {20, 10, 19}, W = {65, 20, 35} ∗ Solution X = {1, 1, 1} is not feasible.