Traveling salesman-based curve reconstruction in polynomial time
An instance of the curve reconstruction problem is a finite sample set V of an unknown collection of curves. The task is to connect the points in V in the order in which they lie on gamma. Giesen [ Proceedings of the 15th Annual ACM Symposium on Computational Geometry (SCG '99), 1999, pp. 207-216] showed recently that the traveling salesman tour of V solves the reconstruction problem for single closed curves under otherwise weak assumptions on gamma and V; gamma must be a single closed curve. We extend his result along several directions: we weaken the assumptions on the sample; we show that traveling salesman-based reconstruction also works for single open curves (with and without specified endpoints) and for collections of closed curves; we give alternative proofs; and we show that in the context of curve reconstruction, the traveling salesman tour can be constructed in polynomial time.
traveling salesman curve reconstruction polynomial time