Salesman simplified?

May 2015
Arlington, VA
Is it helpful to reduce the Travelling Salesman (TS) problem by considering those cities neighboring closest to each other in each of n similar but separate groups, numbering approximately the logarithm of the conventional route permutations?

Recall Stirling's approximation: ln|n!|=n*ln|n|-n.

I believe that in many instances, allocating the total number of cities to the n separate but essentially equal groups, then treating each group as a city of a modified TS, one may use n!>>(n/2)!*(n/2)! for specifically two groups, n!>>(n/3)!*(n/3)!*(n/3)! for specifically three groups, etc. Reducing the factorial argument greatly saves computational complexity.