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On the complexity of approximating Euclidean traveling salesman tours and minimum spanning trees

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44283

Das,  Gautam
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44728

Kapoor,  Sanjiv
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45509

Smid,  Michiel
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Fulltext (public)

1996-1-006
(Any fulltext), 10KB

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Citation

Das, G., Kapoor, S., & Smid, M.(1996). On the complexity of approximating Euclidean traveling salesman tours and minimum spanning trees (MPI-I-1996-1-006). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-A1A1-6
Abstract
We consider the problems of computing $r$-approximate traveling salesman tours and $r$-approximate minimum spanning trees for a set of $n$ points in $\IR^d$, where $d \geq 1$ is a constant. In the algebraic computation tree model, the complexities of both these problems are shown to be $\Theta(n \log n/r)$, for all $n$ and $r$ such that $r<n$ and $r$ is larger than some constant. In the more powerful model of computation that additionally uses the floor function and random access, both problems can be solved in $O(n)$ time if $r = \Theta( n^{1-1/d} )$.