Finding thek smallest spanning trees

@article{Eppstein1992FindingTS,
  title={Finding thek smallest spanning trees},
  author={David Eppstein},
  journal={BIT Numerical Mathematics},
  year={1992},
  volume={32},
  pages={237-248}
}
  • D. Eppstein
  • Published 1 May 1992
  • Computer Science, Mathematics
  • BIT Numerical Mathematics
We give improved solutions for the problem of generating thek smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes timeO(m logβ(m, n)=k2); for planar graphs this bound can be improved toO(n+k2). We also show that thek best spanning trees for a set of points in the plane can be computed in timeO(min(k2n+n logn,k2+kn log(n/k))). Thek best orthogonal spanning trees in the plane can be found in timeO(n logn+kn log log(n/k)+k2). 

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