# 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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#### References

SHOWING 1-10 OF 25 REFERENCES
New Approximation Algorithms for Minimum Cycle Bases of Graphs
• Mathematics, Computer Science
• Algorithmica
• 2009
A Faster Algorithm for Minimum Cycle Basis of Graphs
• Computer Science, Mathematics
• ICALP
• 2004
When Do Short Cycles Generate the Cycle Space?
• Computer Science, Mathematics
• J. Comb. Theory, Ser. B
• 1993
Minimum Path Bases
Algorithms for Generating Fundamental Cycles in a Graph
• Mathematics, Computer Science
• TOMS
• 1982
All-pairs small-stretch paths
• Mathematics, Computer Science
• SODA '97
• 1997
All Pairs Shortest Paths for Graphs with Small Integer Length Edges
• Mathematics, Computer Science
• J. Comput. Syst. Sci.
• 1997