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." J. Appl. Probab. 51 (1) 106 - 117, March 2014. https://doi.org/10.1239/jap/1395771417