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We study a parameter (σ)dependent relaxation of the Travelling Salesman Problem on $\mathbb{R}^2$ .The relaxed problem is reduced to the Travelling Salesman Problemas $\sigma\rightarrow$ 
0. For increasing σ it is also anordered clustering algorithm for a set of points in $\mathbb{R}^2$ .A dual formulation is introduced, which reduces the problem to aconvex optimization, provided the minimizer is in the domain ofconvexity of the relaxed functional. It is shown that this lastcondition is generically satisfied, provided σ is largeenough.
