# Minimum Cycle Basis, Algorithms & Applications

@inproceedings{Michail2006MinimumCB, title={Minimum Cycle Basis, Algorithms \& Applications}, author={D. Michail and M. Bl{\"a}ser and K. Mehlhorn}, year={2006} }

We consider the problem of computing a minimum cycle basis of an undirected 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 F2 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 of its cycle space. A cycle basis where the sum of the weights of its cycles is minimum is called a minimum cycle basis of G. Minimum cycle bases are… Expand

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