Finding the Population Variance of Costs over the Solution Space of the TSP in Polynomial Time
نویسندگان
چکیده
We give a polynomial time algorithm to find the population variance of tour costs over the solution space of the symmetric Traveling Salesman Problem (TSP). In practical terms the algorithm provides a linear time method, on the number of edges of the problem, for determining the standard deviation of these costs. Application of the algorithm has produced empirical evidence that there is a clear relationship between the optimal tour cost and the standard deviation. This suggests that there may be a polynomial time algorithm to estimate the likely optimal tour cost of a TSP. The method for finding the variance also shows promise of being generalizable to higher statistical moments. Key–Words: Traveling salesman problem, Combinatorial optimization, Variance, Standard deviation, Probability distributions, Moments
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