Fast Exact Method for Solving the Travelling Salesman Problem

Let apply this cutting procedure for ... 3 2 1 − − − → → N N N R R R sub-routes. One can readily see that there will be progressive increasing in the disturbances of sub-routes length, i.e. | ) ( ) ( | | ) ( ) ( | 1 1 − + − ≤ − k k k k R D R D R D R D , ,... 3 , 2 − − = N N k As result of application these transformations sequence, we should obtain N P r r r r R ∈ = 2 1 2 1 2 , }, , { sub-route, points of which must satisfy ) , ( max ) , ( 2 1 , 2 1 2 1 p p d r r d N P p p ∈ = condition.