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selection of right points at each step is the basis of success of the method described. One last point about the tour being optimal, after each step we reject C(n,2) longer tours. In next step we again reject approximately C(n,2) tours. Note that the total tours rejected are C(n,2).C(n,2)
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i.e. C(n, 2)
2 but total calculations are 2.C(n,2).Hence in n steps we reject C(n, 2) n (don’t bother
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many tours are common!) but total calculation are no more than n.C(n,2).Mathematically speaking with a check of polynomial origin we can effectively check tours of the range on non polynomial nature. The method succeeds only because it tries to transform multiplication involved in the formulation of solution (that is listing of all possible tours) to addition.