Approximation results toward nearest neighbor heuristic

In this paper, we revisit the famous heuristic called nearest neighbor (NN) for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs belong to interval [a;ta] for a > 0 and t > 1, which certainly corresponds to practical cases of these problems. We prove that NN is a (t + 1)/2t-approximation for maxTSP[a;ta] and a 2/(t + 1)-approximation for min TSP[a;ta] under the standard performance ratio. Moreover, we show that these ratios are tight for some instances.