The Greedy and Delaunay triangulations are not bad in the average case
Information Processing Letters
A non-Hamiltonian, nondegenerate Delaunay Triangulation
Information Processing Letters
There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
The Travelling Salesman and the Pq-Tree
Mathematics of Operations Research
Separating Maximally Violated Comb Inequalities in Planar Graphs
Mathematics of Operations Research
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Separating a Superclass of Comb Inequalities in Planar Graphs
Mathematics of Operations Research
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Exact algorithms for the Hamiltonian cycle problem in planar graphs
Operations Research Letters
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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. Scope and purpose: The traveling salesman problem (TSP) is a fundamental and well-known problem in combinatorial optimisation. It has many applications, for example in vehicle routing and machine scheduling. This paper proposes several heuristics methods for the Euclidean TSP, based on the use of triangulations, and gives extensive computational results.