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In this work we consider the  mean-field traveling salesman problem , where the intercity distances are taken to be independent and identically distributed with some distribution  F . We consider the simplest approximation algorithm, namely, the  nearest-neighbor algorithm , where the rule is to move to the nearest nonvisited city. We show that the limiting behavior of the total length of the nearest-neighbor tour depends on the scaling properties of the density of  F  at 0 and derive the limits for all possible cases of general  F .

On the Nearest-Neighbor Algorithm for the Mean-Field Traveling Salesman Problem