A key point for implementing a fast and efficient local search is to use a neighbourhood of limited size containing all the pertinent moves. For the travelling salesman problem, the most efficient neighbourhoods are based on Lin-Kernighan moves. In order to speed-up the computation, only a subset of moves are evaluated. This article propose a method with a low algorithmic complexity for generating a limited subset of pertinent edges that must be used in the solution tour. Combined with a state-of-the art local search, this technique is able to produce solutions of very high quality to very large problem instances.