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Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) independently distributedin the unit square~\(S,\) each according to a distribution~\(f\) andlet~\(K_n\) be the complete graph formed by joining each pair of nodes by astraight line segment. For every edge~\(e\) in~\(K_n\) we associate aweight~\(w(e)\) that may depend on the \emph{individual locations} of theendvertices of~\(e\) and is not necessarily a power of the Euclidean lengthof~\(e.\) Denoting~\(TSP_n\) to be the minimum weight of a spanning cycleof~\(K_n\) corresponding to the travelling salesman problem (TSP) and assumingan equivalence condition on the weight function~\(w(.),\) we provethat~\(TSP_n\) appropriately scaled and centred converges to zero a.s.\ and inmean as~\(n \rightarrow \infty.\) We also obtain upper and lower bounddeviation estimates for~\(TSP_n.\)

Euclidean traveling salesman problem with location dependent and power weighted edges