Worst-case examples for the spacefilling curve heuristic for the Euclidean traveling salesman problem

Authors:
Dimitris Bertsimas;Michelangelo Grigni
Affiliations:
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Venue:
Operations Research Letters
Year:
1989

Citing 4
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Abstract

Bartholdi and Platzman [3] proposed the spacefilling curve heuristic for the Euclidan Traveling Salesman Problem and proved that their heuristic returns a tour within an O(lg n)factor of optimal length. They conjectured that the worst-case ratio is in fact O(1). In this note a counterexample is exhinited showing the O(lg n) upper bound is tight.