Finding the population variance of costs over the solution space of the TSP in polynomial time

Authors:
Paul John SutcLiffe;Andrew Solomon;Jenny Edwards
Affiliations:
University of Technology, Sydney, Faculty of Information Technology, Broadway, Sydney, Australia;University of Technology, Sydney, Faculty of Information Technology, Broadway, Sydney, Australia;University of Technology, Sydney, Faculty of Information Technology, Broadway, Sydney, Australia
Venue:
MATH'07 Proceedings of the 11th WSEAS International Conference on Applied Mathematics
Year:
2007

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Abstract

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.