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MPI-I-96-1-006

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

Das, Gautam and Kapoor, Sanjiv and Smid, Michiel

MPI-I-96-1-006. March 1996, 14 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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 $r = \Theta( n^{1-1/d} )$.
Acknowledgement:
References to related material:


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URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1996-1-006
Hide details for BibTeXBibTeX
@TECHREPORT{DasKapoorSmid96,
  AUTHOR = {Das, Gautam and Kapoor, Sanjiv and Smid, Michiel},
  TITLE = {On the complexity of approximating Euclidean traveling salesman tours and minimum spanning trees},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-96-1-006},
  MONTH = {March},
  YEAR = {1996},
  ISSN = {0946-011X},
}