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Good triangulations yield good tours

Research output: Contribution to journalJournal article

Published

Journal publication date2008
JournalComputers and Operations Research
Journal number2
Volume35
Number of pages10
Pages638-647
Original languageEnglish

Abstract

Consider the following heuristic for planar Euclidean instances of the Traveling Salesman Problem (TSP): select a subset of the edges which induces a planar graph, and solve either the TSP or its graphical relaxation on that graph. In this paper, we give several motivations for considering this heuristic, along with extensive computational results. It turns out that the Delaunay and greedy triangulations make effective choices for the induced planar graph. Indeed, our experiments show that the resulting tours are on average within 0.1% of optimality.