@techreport{DasKapoorSmid96,
TITLE = {On the complexity of approximating Euclidean traveling salesman tours and minimum spanning trees},
AUTHOR = {Das, Gautam and Kapoor, Sanjiv and Smid, Michiel},
LANGUAGE = {eng},
NUMBER = {MPI-I-1996-1-006},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {1996},
DATE = {1996},
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 $r = \Theta( n^{1-1/d} )$.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}