A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid

@inproceedings{Golynski2002APT,
  title={A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid},
  author={Alexander Golynski and Joseph Douglas Horton},
  booktitle={SWAT},
  year={2002}
}
The Minimal Cycle Basis Problem (MCB) is the following. Given a binary matroid with nonnegative weights assigned to its elements, what is the set of cycles with total smallest weight which generate all of the circuits of the matroid? The answer to this problem also answers in some cases the Sparsest Null Space Basis Problem (NSP) [CP87]. Given a t n matrix A with t < n and rank r, nd a matrix N with the fewest nonzeros whose columns span the null space of A. Coleman and Pothen nd solutions to… CONTINUE READING
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