Worst-case examples for the spacefilling curve heuristic for the Euclidean Travelling Salesman Problem

Worst-case examples for the spacefilling curve heuristic for the Euclidean Travelling Salesman Problem

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Article ID: iaor19891006
Country: Netherlands
Volume: 8
Issue: 5
Start Page Number: 241
End Page Number: 244
Publication Date: Oct 1989
Journal: Operations Research Letters
Authors: ,
Keywords: programming: travelling salesman
Abstract:

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

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