These are the steps of the algorithm: The sequence of the
visited vertices is the output of the algorithm. The nearest
neighbour algorithm is easy to implement and executes quickly,
but it can sometimes miss shorter routes which are easily
noticed with human insight, due to its "greedy" nature. As a
general guide, if the last few stages of the tour are comparable
in length to the first stages, then the tour is reasonable; if
they are much greater, then it is likely that there are much
better tours. Another check is to use an algorithm such as the
lower bound algorithm to estimate if this tour is good enough.
In the worst case, the algorithm results in a tour that is much
longer than the optimal tour. To be precise, for every constant
r there is an instance of the traveling salesman problem such
that the length of the tour length computed by the nearest
neighbour algorithm is greater than r times the length of the
optimal tour. Moreover, for each number of cities there is an
assignment of distances between the