I'm working on a path planning algorithm that is equivalent to a traveling salesman problem. I don't know how many nodes I might have so I'm willing to sacrifice accuracy for speed. My problem can be modeled as a fully connected graph, with the cost of transitioning between nodes being related to more than just the distance between nodes. I'd like to restrict my search space to connections that lie on the delaunay triangulation (the research I've read notes that 95-100% of connections in solutions to the TSP lie on the delaunay triangulation) but since my graph cannot be expressed as 2D or even 3D geometry, I can't directly use it in my representation. Is there an algorithm that results in an equivalent triangulation to the delaunay triangulation that applies to graphs that do not conform to a geometric representation (cost of connections cannot be expressed as a geometric distance between points due to over-constraint)?
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Don't get why are you need to use 3D geometry? Per wiki it can be done on the plane. – Dewfy Apr 17 '12 at 16:31
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The nodes themselves exist in 3d but the cost is not completely based on distance. The graph itself cannot be expressed as 2d or even 3d geometry because the connections between nodes are over-constrained. I know the triangulation can be found for a plane or even an 3d hyperplane, but I need an equivalent representation for n-dimensional geometry. – Alex Londeree Apr 17 '12 at 16:43
