Approximation results toward Nearest Neighbor heuristic

Jérôme Monnot (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

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 Max TSP[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.

Domaines: Mathématique discrète [cs.DM]

Jérôme Monnot. Approximation results toward Nearest Neighbor heuristic. Yugoslav Journal of Operations Research, 2002, 12, pp.11-16. ⟨hal-00004012⟩