What is meant by approximation algorithm?
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one.
Can approximate algorithm be better than exact algorithm?
Exact algorithms can find the optimum solution with precision. Approximate algorithms can find a near optimum solution. The main difference is that exact algorithms apply in “easy” problems.
What is metric TSP problem?
The Metric Travelling Salesman Problem is a subcase of the Travel- ling Salesman Problem (TSP), where the triangle inequality holds. It is a key problem in combinatorial optimization. Solutions of the Metric TSP are gener- ally used for costs minimization tasks in logistics, manufacturing and genetics.
Is TSP strongly NP hard?
TSP is strongly NP-hard. Let G be an undirected graph in which we want to find the Hamiltonian circuit. Create a TSP instance such that every node from G is associated to one node in the complete undirected graph Kn.
Which one is a better approximation algorithms?
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.
Which one is better approximation algorithm?
Are heuristics better than algorithms?
While algorithms provide step-by-step procedures that can guarantee solutions, heuristics are faster and provide shortcuts for getting to solutions, though this has the potential to cause errors.
What is the 2 approximation algorithm for TSP?
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).
Is there a TSP algorithm for the travelling salesman problem?
Travelling Salesman Problem Metric TSP 15 Concluding Remarks There is a polynomial-time3 2 -approximation algorithm for the travelling salesman problem with the triangle inequality. Theorem (Christofides’76) There is a PTAS for theEuclidean TSP Problem. Theorem (Arora’96, Mitchell’96)
Is there a polynomial time 3 2-approximation algorithm for travelling salesman?
8:returnH There is a polynomial-time3 2 -approximation algorithm for the travelling salesman problem with the triangle inequality. Theorem (Christofides’76) VI. Travelling Salesman Problem Metric TSP 13
What is the triangle-inequality algorithm for TSP?
The Triangle-Inequality holds in many practical situations. When the cost function satisfies the triangle inequality, we can design an approximate algorithm for TSP that returns a tour whose cost is never more than twice the cost of an optimal tour. The idea is to use M inimum S panning T ree (MST). Following is the MST based algorithm.