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#### Traveling Salesman-Based Curve Reconstruction in Polynomial Time

##### MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44003

Althaus,  Ernst
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Zitation

Althaus, E., & Mehlhorn, K. (2001). Traveling Salesman-Based Curve Reconstruction in Polynomial Time. SIAM Journal on Computing, 31, 27-66.

An instance of the curve reconstruction problem is a finite sample set $V$ of an unknown curve $\gamma$. The task is to connect the points in $V$ in the order in which they lie on $\gamma$. Giesen~\cite{Giesen:TSP} showed recently that the Traveling Salesman tour of $V$ solves the reconstruction problem under fairly week assumptions on $\gamma$ and $V$. We extend his result along three dimensions. We weaken the assumptions, give an alternate proof, and show that in the context of curve reconstruction, the Traveling Salesman tour can be constructed in polynomial time.