Natural Greedy Heuristic

Recently quantum annealing is well known as Traveling salesman problem.

It must be P=NP.

The symmetric matrix means that the cost of traveling from city i to city j is equal to the cost of traveling from j to i. This is Zero, and Hamiltonian cycle is undirected complete graph with a cost associated with each edge.

You can choose any start points, which is Φ. It must be P≠NP.

This is natural greedy heuristic, because j is added to the cycle.

cik≤cij+cjk

i∈S and j∉S (S is the subset)

G=(V,E)

This is the undirected graph.

F⊆E

F is the minimal subset of edges, and each pair of nodes in G is connected.

S={v}, v∈V, T=(S,F), F=Φ

T is a tree, and v is an arbitrary node.

The metric traveling salesman problem is a 2-approximation algorithm.

The cost of the tour on the first two nodes i and j is exactly 2cij.

△ijk is the triangle, and the perfect matching on Θ has cost at most OPT/2. It is not the odd number.

Skipping over previously visited cities is sometimes called shortcutting.

This is Φ=0, which is corruption and wide open.