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Short abstract, isnt it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers ...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could possibly enumerate 10 9 tours per second on a computer it would thus take roughly 10 639 years of computing to establish the optimality of this tour by exhaustive enumeration. This quote shows the real difficulty of a combinatorial optimization problem. The huge number of configurations is the primary difficulty when dealing with one of these problems. The quote belongs to M.W Padberg and M. Grotschel, Chap. 9., Polyhedral computations, from the book The Traveling Salesman Problem: A Guided tour of Combinatorial Optimization 124. It is interesting to compare the number of configurations of real-world problems in combinatorial optimization with those large numbers arising in Cosmol...
Pablo Moscato (Sun,) studied this question.