A Constant-Factor Approximation Algorithm for the Geometric k-MST Problem in the Plane

@article{Mitchell1998ACA,
  title={A Constant-Factor Approximation Algorithm for the Geometric k-MST Problem in the Plane},
  author={Joseph S. B. Mitchell and Avrim Blum and Prasad R. Chalasani and Santosh S. Vempala},
  journal={SIAM J. Comput.},
  year={1998},
  volume={28},
  pages={771-781}
}
We show that any rectilinear polygonal subdivision in the plane can be converted into a "guillotine" subdivision whose length is at most twice that of the original subdivision. "Guillotine" subdivisions have a simple recursive structure that allows one to search for "optimal" such subdivisions in polynomial time, using dynamic programming. In particular, a consequence of our main theorem is a very simple proof that the k-MST problem in the plane has a constant-factor polynomial-time… 

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