Question

Given Problem:
1. A traveling salesman wants to visit each of n cities exactly once and return to its starting point with minimum distance/mileage covered.
Question:
1. What are the vertices from the given problem?
2. What is the edge from the given problem?
3. What is the shortest path to travel all of the cities once and return to its starting point?

Answer 1

Answer:

vivkkvvkkvkvkbbkbkbkbkbkbkkbbkbkkb

Answer 2

Answer:

Travelling Salesman Problem (TSP): Given a set of cities and distance between every pair of cities, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point.

Note the difference between Hamiltonian Cycle and TSP. The Hamiltoninan cycle problem is to find if there exist a tour that visits every city exactly once. Here we know that Hamiltonian Tour exists (because the graph is complete) and in fact many such tours exist, the problem is to find a minimum weight Hamiltonian Cycle.

Euler1