An O(log k) approximation algorithm for the k minimum spanning tree problem in the plane

@inproceedings{Garg1994AnOK,
  title={An O(log k) approximation algorithm for the k minimum spanning tree problem in the plane},
  author={Naveen Garg and Dorit S. Hochbaum},
  booktitle={STOC},
  year={1994}
}
A cable company is permitted to service k cities in a state with n cities. To minimise the cost of installation the company wishes to find a set of cities that are “close”. Since we need to connect these cities, a natural measure of “closeness” is the weight of the minimum tree spanning them where the weight of the edge (i, ~) is the euclidean dist ante, d(i, ~), between cities i and ~. More formally, the problem that we address in this paper is the following. 
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Spanning trees short and small

  • R. Ravi, R. Sundaram, M. V. Marathe, D. J. Rosenkrantz, S. S. Ravi
  • Proceedings, 5th Annual ACM-SIAM Symposium on…
  • 1993
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