Counting Minimum Weight Spanning Trees

@article{Broder1997CountingMW,
  title={Counting Minimum Weight Spanning Trees},
  author={Andrei Z. Broder and Ernst W. Mayr},
  journal={J. Algorithms},
  year={1997},
  volume={24},
  pages={171-176}
}
We present an algorithm for counting the number of minimum weight spanning trees, based on the fact that the generating function for the number of spanning trees of a given graph, by weight, can be expressed as a simple determinant. For a graph with n vertices and m edges, our algorithm requires O(M(n)) elementary operations, whereM(n) is the number of elementary operations needed to multiply n n matrices. The previous best algorithm for this problem, due to Gavril [3], required O(nM(n… CONTINUE READING

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