On the nearest neighbor rule for the traveling salesman problem

Authors:
Cor A. J. Hurkens;Gerhard J. Woeginger
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands;Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Venue:
Operations Research Letters
Year:
2004

Citing 0
Cited 5

A hybrid scatter search for the probabilistic traveling salesman problem

Computers and Operations Research
An Evolutionary Algorithm with Diversified Crossover Operator for the Heterogeneous Probabilistic TSP

MDAI '07 Proceedings of the 4th international conference on Modeling Decisions for Artificial Intelligence
Online graph exploration: new results on old and new algorithms

ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Online graph exploration with advice

SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Online graph exploration: New results on old and new algorithms

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Rosenkrantz et al. (SIAM J. Comput. 6 (1977) 563) and Johnson and Papadimitriou (in: E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, D.B. Shmoys (Eds.), The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley, Chichester, 1985, pp. 145-180, (Chapter 5)) constructed families of TSP instances with n cities for which the nearest neighbor rule yields a tour-length that is a factor @W(logn) above the length of the optimal tour. We describe two new families of TSP instances, for which the nearest neighbor rule shows the same bad behavior. The instances in the first family are graphical, and the instances in the second family are Euclidean. Our construction and our arguments are extremely simple and suitable for classroom use.