An $\tilde{O}(m^{2}n)$ Algorithm for Minimum Cycle Basis of Graphs

@article{Kavitha2007An,
  title={An 
\$\tilde\{O\}(m^\{2\}n)\$ 
Algorithm for Minimum Cycle Basis of Graphs},
  author={T. Kavitha and K. Mehlhorn and D. Michail and Katarzyna E. Paluch},
  journal={Algorithmica},
  year={2007},
  volume={52},
  pages={333-349}
}
Abstract We consider the problem of computing a minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over $\mathbb{F}_{2}$ generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle… Expand
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