# Minimum cycle bases: Faster and simpler

@article{Mehlhorn2009MinimumCB, title={Minimum cycle bases: Faster and simpler}, author={K. Mehlhorn and D. Michail}, journal={ACM Trans. Algorithms}, year={2009}, volume={6}, pages={8:1-8:13} }

We consider the problem of computing exact or approximate minimum cycle bases of an undirected (or directed) graph <i>G</i> with <i>m</i> edges, <i>n</i> vertices and nonnegative edge weights. In this problem, a {0, 1} (−1,0,1}) incidence vector is associated with each cycle and the vector space over F<sub>2</sub> (Q) generated by these vectors is the cycle space of <i>G</i>. A set of cycles is called a cycle basis of <i>G</i> if it forms a basis for its cycle space. A cycle basis where the sum… Expand

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#### References

SHOWING 1-5 OF 5 REFERENCES

A Polynomial-Time Algorithm to Find the Shortest Cycle Basis of a Graph

- Mathematics, Computer Science
- SIAM J. Comput.
- 1987

A greedy approach to compute a minimum cycle basis of a directed graph

- Mathematics, Computer Science
- Inf. Process. Lett.
- 2005

Faster Algorithms for Approximate Distance Oracles and All-Pairs Small Stretch Paths

- Mathematics, Computer Science
- 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
- 2006

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

- Mathematics, Computer Science
- SWAT
- 2002