## How do you do Christofides algorithm?

Algorithm

- Create a minimum spanning tree T of G.
- Let O be the set of vertices with odd degree in T.
- Find a minimum-weight perfect matching M in the induced subgraph given by the vertices from O.
- Combine the edges of M and T to form a connected multigraph H in which each vertex has even degree.

## What is the time complexity of Travelling Salesman Problem?

There are at most O(n*2n) subproblems, and each one takes linear time to solve. The total running time is therefore O(n2*2n). The time complexity is much less than O(n!), but still exponential. Space required is also exponential.

**Has anyone solved the traveling salesman problem?**

Scientists in Japan have solved a more complex traveling salesman problem than ever before. The previous standard for instant solving was 16 “cities,” and these scientists have used a new kind of processor to solve 22 cities. They say it would have taken a traditional von Neumann CPU 1,200 years to do the same task.

**What is Travelling Salesman Problem explain with example?**

The traveling salesman problem (TSP) is an algorithmic problem tasked with finding the shortest route between a set of points and locations that must be visited. In the problem statement, the points are the cities a salesperson might visit.

### Why is TSP not in NP?

Why is TSP not NP-complete? The simple answer is that it’s NP-hard, but it’s not in NP. Since it’s not in NP, it can’t be NP-complete. In TSP you’re looking for the shortest loop that goes through every city in a given set of cities.

### Why do we use approximation algorithms?

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.